Question 1

In this divisibility based odd one out question, select the number that is not divisible by 3 among 462, 297, 674 and 891.

Accepted Answer

Introduction / Context:This question is from the number system and divisibility chapter. You must decide which of the four given numbers is not a multiple of 3. Divisibility by 3 can be checked quickly using the digit sum rule, making this a classic and important pattern used in many aptitude tests.Given Data / Assumptions:The numbers are 462, 297, 674 and 891.We use the standard divisibility rule for 3: a number is divisible by 3 if the sum of its digits is divisible by 3.The odd one out will be the only number whose digit sum is not divisible by 3.Concept / Approach:Instead of dividing each number by 3, we apply the digit sum test. We add the digits of each number and see whether the result is a multiple of 3. If three numbers pass this test and one fails, the failing number is the odd one out.Step-by-Step Solution:Step 1: For 462, digits are 4, 6 and 2. Sum = 4 + 6 + 2 = 12. Since 12 is divisible by 3, 462 is divisible by 3.Step 2: For 297, digits are 2, 9 and 7. Sum = 2 + 9 + 7 = 18. Since 18 is divisible by 3, 297 is divisible by 3.Step 3: For 891, digits are 8, 9 and 1. Sum = 8 + 9 + 1 = 18. Since 18 is divisible by 3, 891 is divisible by 3.Step 4: For 674, digits are 6, 7 and 4. Sum = 6 + 7 + 4 = 17. Since 17 is not divisible by 3, 674 is not divisible by 3.Step 5: Since 462, 297 and 891 are divisible by 3 and 674 is not, 674 is the odd one out.Verification / Alternative check:If you prefer direct division, you can compute 462 / 3 = 154, 297 / 3 = 99 and 891 / 3 = 297, all integers. For 674 / 3, you get approximately 224.67, which is not an integer. This numerical check matches the conclusion from the digit sum method and confirms that 674 is not a multiple of 3.Why Other Options Are Wrong:462 is not the odd one out because it is clearly a multiple of 3.297 is also divisible by 3 and therefore belongs with 462 and 891.891 is divisible by 3, so it also follows the common pattern and is not unique.Common Pitfalls:A common pitfall is misadding digits under exam pressure, which can lead to an incorrect conclusion about divisibility. Another mistake is to rely solely on the fact that a number is even or ends in certain digits, which is not relevant to divisibility by 3. Practicing the digit sum rule carefully and double checking simple additions can prevent these errors.Final Answer:The only number not divisible by 3 is 674, so 674 is the odd one out.

Question 2

In this disease based odd one out question, select the disease that is not primarily transmitted by mosquitoes among Tuberculosis, Chikungunya, Malaria and Dengue.

Accepted Answer

Introduction / Context:This question lies in the general science and health awareness category. You are asked to identify which disease among the four options is not primarily mosquito borne. Public health and disease transmission mode awareness are important topics in many general knowledge and competitive examinations.Given Data / Assumptions:The diseases listed are Tuberculosis, Chikungunya, Malaria and Dengue.We consider the main mode of transmission for each disease.We assume standard medical knowledge about common infectious diseases.Concept / Approach:The idea is to recall how each disease spreads. Chikungunya, Malaria and Dengue are all widely known to be transmitted by mosquitoes. Tuberculosis, however, is transmitted mainly through airborne droplets when an infected person coughs or sneezes. Therefore, the disease that is not mosquito borne is the odd one out.Step-by-Step Solution:Step 1: Chikungunya is a viral disease transmitted to humans by the bite of infected Aedes mosquitoes.Step 2: Malaria is a parasitic disease transmitted by the bite of infected female Anopheles mosquitoes.Step 3: Dengue is another viral infection transmitted by Aedes mosquitoes, especially Aedes aegypti.Step 4: Tuberculosis is a bacterial infection caused by Mycobacterium tuberculosis, typically spread through airborne droplets from an infected person and not through mosquito bites.Step 5: Since Chikungunya, Malaria and Dengue are mosquito borne diseases and Tuberculosis is not, Tuberculosis is the odd one out.Verification / Alternative check:You can verify by recalling common public health messages and campaigns. Malaria and Dengue are often mentioned together in mosquito control initiatives. Chikungunya is also discussed alongside other mosquito transmitted diseases. Tuberculosis campaigns focus on covering mouths while coughing, diagnosis, medication adherence and respiratory transmission, showing that its mode of spread is different from mosquito borne diseases.Why Other Options Are Wrong:Chikungunya is not the odd one out because it is clearly transmitted by mosquitoes.Malaria is a classic mosquito borne disease, making it part of the majority group.Dengue is again a mosquito transmitted disease and therefore not the unique option.Common Pitfalls:Some candidates may not recall exactly how each disease spreads and might guess based on familiarity of names. Another pitfall is confusing diseases that share symptoms such as fever and body aches but differ in transmission mode. To avoid confusion, it is useful to revise major diseases along with their mode of transmission and preventive measures.Final Answer:The only disease that is not primarily mosquito borne is Tuberculosis, so Tuberculosis is the odd one out.

Question 3

In each of the following three letter groups, the letters follow a certain positional pattern in the English alphabet. Select the group of letters that is the odd one out because it does not follow the same pattern as the other three.

Accepted Answer

Introduction / Context:This reasoning question is based on alphabetical patterns in three letter groups. Three of the options follow the same pattern when you look carefully at the positions of the letters in the English alphabet, while one option breaks that pattern. Your task is to identify the group of letters that is the odd one out. Such questions are common in competitive exams to test attention to detail, pattern recognition, and basic familiarity with the alphabetical order.
Given Data / Assumptions:- We use the standard English alphabet from A to Z with positions A = 1, B = 2, C = 3 and so on up to Z = 26.- The four options are three letter groups: FHG, NOP, TVU, and WYX.- We assume that the pattern, if any, is created by moving forward or backward by a fixed number of positions in the alphabet.- The odd group will be the one that does not follow the same movement pattern as the others.
Concept / Approach:The key idea is to convert each letter into its numerical position in the alphabet and then analyze how the second and third letters are obtained from the first letter. If most options follow one type of movement, such as plus two then minus one, and only one option has a different movement, that option is the odd one out.
Step-by-Step Solution:Step 1: For FHG, positions are F = 6, H = 8, G = 7. From 6 to 8 we move +2, and from 8 to 7 we move -1.Step 2: For NOP, positions are N = 14, O = 15, P = 16. From 14 to 15 we move +1, and from 15 to 16 we again move +1.Step 3: For TVU, positions are T = 20, V = 22, U = 21. From 20 to 22 we move +2, and from 22 to 21 we move -1.Step 4: For WYX, positions are W = 23, Y = 25, X = 24. From 23 to 25 we move +2, and from 25 to 24 we move -1.Step 5: Compare the movement patterns. Three options follow +2 then -1, while one option follows +1 then +1.
Verification / Alternative check:We can verify our conclusion by rewriting the movements in a compact form. FHG, TVU, and WYX all follow the pattern first letter +2 gives second letter, and second letter -1 gives third letter. NOP progresses as first letter +1 gives second letter, and second letter +1 gives third letter. Since this is clearly different, NOP is the odd group.
Why Other Options Are Wrong:FHG is not odd because it fits the +2 then -1 pattern. TVU also fits the same +2 then -1 pattern. WYX again follows the same +2 then -1 movement. Since these three share a common rule, they cannot be considered the odd ones out. Only NOP violates that rule.
Common Pitfalls:Many learners quickly focus on whether the letters are in alphabetical order or reversed, instead of looking at the exact numerical differences. Another common mistake is to consider that NOP looks simple and regular, so it must be correct, when in fact the correct approach is to find the majority pattern and then highlight the one that does not follow that majority. Forgetting to convert letters into positions can also make the pattern hard to see.
Final Answer:The odd group of letters is NOP, because it follows a +1, +1 pattern, while all the other groups follow a +2, -1 pattern.

Question 4

Each of the following is a four digit number in which the first two digits are somehow related to the last two digits. By examining the pattern between the first pair and the last pair of digits, select the number that is the odd one out.

Accepted Answer

Introduction / Context:This is a typical odd one out question based on number patterns. The four digit numbers seem similar at first glance, but there is a hidden relationship between the first two digits and the last two digits in most of the options. Your job is to discover this relationship and then find the number that does not follow it. Such questions are widely used in aptitude tests to assess numerical pattern recognition and logical thinking.
Given Data / Assumptions:- The given numbers are 8715, 5712, 9817, and 6812.- Each number can be thought of as composed of two parts: the first two digits and the last two digits.- We assume there is a simple arithmetic relation, such as addition, between the first pair of digits and the last pair of digits.
Concept / Approach:The most natural approach is to split each four digit number into two parts and check whether the last two digits can be obtained from the first two digits by applying a simple operation. A very common pattern in such questions is that the last two digits equal the sum of the first two digits, written as a two digit number. If three numbers obey this pattern and one does not, then the one that breaks the rule is the odd one out.
Step-by-Step Solution:Step 1: Consider 8715. Add the first two digits: 8 + 7 = 15. The last two digits are 15, so the pattern holds.Step 2: Consider 5712. Add the first two digits: 5 + 7 = 12. The last two digits are 12, so the pattern again holds.Step 3: Consider 9817. Add the first two digits: 9 + 8 = 17. The last two digits are 17, so the pattern holds here as well.Step 4: Consider 6812. Add the first two digits: 6 + 8 = 14. However, the last two digits are 12, not 14. This number does not follow the same rule.Step 5: Conclude that 6812 is the only number that breaks the pattern sum of first two digits equals the last two digits.
Verification / Alternative check:We can double check by explicitly writing each number in the form AB and CD. For 8715, AB = 87 and CD = 15, and 8 + 7 = 15. For 5712, 5 + 7 = 12. For 9817, 9 + 8 = 17. Only for 6812 is the sum 6 + 8 equal to 14, which does not match 12. This confirms our conclusion.
Why Other Options Are Wrong:8715 is not the odd one out because its last two digits correctly equal the sum of its first two digits. The same is true for 5712 and 9817; both strictly follow the same rule. Since those three obey the pattern, they must be considered consistent, leaving 6812 as the only inconsistent value.
Common Pitfalls:One common mistake is to look for complicated patterns such as multiplication, division, or positional digit swaps when a very simple addition rule is sufficient. Another error is to add all four digits instead of separating the number into two parts. Candidates sometimes also miscalculate the sums, especially under time pressure, which can lead to a wrong choice. Carefully rechecking the addition for each option avoids this issue.
Final Answer:The odd number is 6812, because it does not satisfy the rule that the last two digits equal the sum of the first two digits.

Question 5

Among the following four numbers, three are perfect squares of positive integers and one number is not a perfect square. By using your knowledge of square numbers, select the number that is the odd one out.

Accepted Answer

Introduction / Context:This question tests your familiarity with perfect squares and your ability to quickly recognize them. In many aptitude exams, you are given a group of numbers where all but one obey a specific property, such as being perfect squares, perfect cubes, or prime numbers. Your task here is to identify which of the four given numbers is not a perfect square. Recognizing square numbers is a useful mental skill in quantitative aptitude, number system questions, and simplification problems.
Given Data / Assumptions:- The numbers given are 961, 443, 361, and 289.- A perfect square is a number that can be written as n^2 for some positive integer n.- We assume standard arithmetic with no tricks or special bases.
Concept / Approach:To solve this, recall commonly used square numbers. For example, 17^2 = 289, 19^2 = 361, and 31^2 = 961. Any number that does not match a known integer square is not a perfect square. It is efficient to remember square values at least up to 35^2 for competitive exams. When in doubt, you can try to approximate the square root and see whether it is an integer.
Step-by-Step Solution:Step 1: Check 289. Since 17 * 17 = 289, this number is a perfect square of 17.Step 2: Check 361. We know that 19 * 19 = 361, so 361 is a perfect square of 19.Step 3: Check 961. Observe that 30^2 = 900 and 31^2 = 961, so 961 is a perfect square of 31.Step 4: Check 443. Nearby squares are 21^2 = 441 and 22^2 = 484. Since 443 is between 441 and 484 and not equal to either, it is not a perfect square.Step 5: Conclude that 443 is the only number among the four that is not a perfect square.
Verification / Alternative check:To verify, we can approximate the square root of 443. It lies between 21 and 22 because 21^2 = 441 and 22^2 = 484. Since there is no integer n such that n^2 = 443, the number cannot be a perfect square. The other three numbers correspond exactly to integer squares that are often memorised for exam practice.
Why Other Options Are Wrong:961 is wrong as the odd one because it clearly equals 31^2, so it satisfies the perfect square property. Similarly, 361 equals 19^2 and 289 equals 17^2, so both are perfect squares. Since these three meet the same condition, they are part of the majority group and cannot be the odd one out.
Common Pitfalls:Students sometimes confuse 289 with 17 * 19 or mix up nearby square values. Another mistake is to stop after checking only one or two numbers and guessing the answer without verifying all options. Some candidates also attempt long division style square root calculations, which is slow under exam constraints. Instead, memorizing square values up to at least 35^2 and using quick comparison with nearby squares is more efficient.
Final Answer:The odd number is 443, because it is not a perfect square, while the other three numbers are perfect squares of 17, 19, and 31 respectively.

Question 6

Two series I and II given below each have one wrong number P and Q respectively.  Series I: 5, 20, 40, 67, 105, 140, 224 Series II: 13, 20, 30, 98, 119, 334  Find the difference between P and Q

Accepted Answer

Concept & Pattern Recognition
To find a wrong number in a series, we calculate the differences between consecutive terms. If the first differences don't show a clear pattern, we calculate the "second differences" (the differences of the differences). Often, these reveal standard sequences like prime numbers, squares, or cubes.

Step-by-Step Solution
Step 1: Analyze Series I to find P
Given Series I: 5, 20, 40, 67, 105, 140, 224
Let's calculate the first level of differences between consecutive terms:
• 20 - 5 = 15
• 40 - 20 = 20
• 67 - 40 = 27
• 105 - 67 = 38
• 140 - 105 = 35
• 224 - 140 = 84

First differences: 15, 20, 27, 38, 35, 84.
Now, let's calculate the second level of differences (for the first few terms):
• 20 - 15 = 5
• 27 - 20 = 7
• 38 - 27 = 11

Notice the sequence 5, 7, 11. These are consecutive prime numbers! 
Following this pattern, the next prime numbers should be 13 and 17.

Let's reconstruct the first differences using these next primes:
• Next first difference should be: 38 + 13 = 51
• The first difference after that should be: 51 + 17 = 68

Now, let's apply these corrected first differences to find the correct terms in the main series:
• Correct 6th term: 105 + 51 = 156
• Let's verify the final term: 156 + 68 = 224. This matches the last term of the series perfectly!
Therefore, the number 140 is incorrect and should be 156. 
So, P = 140.

Step 2: Deduce Q using the given options
We need to find the difference P - Q. Let's test the given options against P = 140 to see which one yields a number that actually exists in Series II (13, 20, 30, 98, 119, 334).
• If P - Q = 24, then 140 - Q = 24 \implies Q = 116 (Not in Series II)
• If P - Q = 36, then 140 - Q = 36 \implies Q = 104 (Not in Series II)
• If P - Q = 38, then 140 - Q = 38 \implies Q = 102 (Not in Series II)
• If P - Q = 42, then 140 - Q = 42 \implies Q = 98 (This number is in Series II!)

Since 98 is a term in Series II, it must be the wrong number Q.

Exam Strategy & Shortcut
Reverse Engineering: In competitive exams, time is your most valuable asset. Once you confidently find P = 140, do not waste time figuring out the complex pattern of Series II. The wrong number Q *must* be one of the numbers explicitly listed in Series II. By subtracting the multiple-choice options from 140, you instantly find that only option (d) results in a number (98) that is present in the second series.

Common Pitfall
A common mistake is stubbornly trying to decode the exact mathematical pattern of the second series when it's not strictly necessary to answer the multiple-choice question. Always let the options guide your logic when you hit a roadblock.

Final Answer
Therefore, the correct answer is 42.

Question 7

Given below three series I, II & III given and each series has a wrong number. The number that should come in place of the wrong number in series I, II & III is P, Q & R respectively. Find the value of P, Q & R and then find which of the following s…

Accepted Answer

Concept & Logical Deduction
To find the wrong numbers in these series, we must identify the underlying mathematical pattern (differences, double differences, or multipliers) for each sequence and replace the anomaly to satisfy the pattern.

Step-by-Step Solution
• Series I: 244, 380, 476, 536, 568, 580, 580
• Calculate the differences between consecutive terms from right to left: 580 - 580 = 0, 580 - 568 = 12, 568 - 536 = 32, 536 - 476 = 60, 476 - 380 = 96.
• Calculate the double differences: 12 - 0 = 12, 32 - 12 = 20, 60 - 32 = 28, 96 - 60 = 36.
• The double differences (12, 20, 28, 36) form an arithmetic progression with a common difference of 8.
• The next double difference should be 36 + 8 = 44.
• The next single difference should be 96 + 44 = 140.
• The first term should be 380 - 140 = 240, not 244.
• Thus, P = 240.
• Series II: 160, 200, 480, 1200, 3600, 12600, 50400
• Calculate the ratio of consecutive terms: 50400 / 12600 = 4, 12600 / 3600 = 3.5, 3600 / 1200 = 3, 1200 / 480 = 2.5.
• The multipliers follow the pattern: 1.5, 2, 2.5, 3, 3.5, 4.
• Let's test this: 160 	imes 1.5 = 240.
• 240 	imes 2 = 480 (This matches the third term).
• Therefore, 200 is the wrong term and should be 240.
• Thus, Q = 240.
• Series III: 15, 20, 36, 65, 111, 186, 264
• Calculate the differences: 20 - 15 = 5, 36 - 20 = 16, 65 - 36 = 29, 111 - 65 = 46.
• Calculate the double differences: 16 - 5 = 11, 29 - 16 = 13, 46 - 29 = 17.
• The double differences are consecutive prime numbers: 11, 13, 17.
• The next prime numbers are 19 and 23.
• The next differences should be 46 + 19 = 65, and 65 + 23 = 88.
• The next terms should be 111 + 65 = 176, and 176 + 88 = 264.
• Therefore, 186 is the wrong term and should be 176.
• Thus, R = 176.
• Conclusion: We have P = 240, Q = 240, and R = 176. This gives the relation P = Q > R.

Exam Strategy & Shortcut
Instead of solving from left to right, start from the right end of a sequence if the numbers are easier to manage or if the pattern becomes clearer. In Series I and II, working backwards quickly revealed the arithmetic and geometric progressions.

Common Pitfall
A common mistake is trying to fit a complex polynomial or power series when a simple double difference or multiplier pattern exists. Always check first and second differences first.

Final Answer
Therefore, the correct answer is P = Q > R.

Question 8

Calculate the value of (A) and (B) and answer the questions given below:  (A), (B), 102, 104, 107, 113, 128, 173  If M is 150% more than (A), then find which of the following number is nearest square root of the difference between M and (B).

Accepted Answer

Concept & Pattern Recognition
To determine the unknown variables in a sequence, extract the differences between the known terms and identify a secondary pattern (such as a multiplicative factor) that defines these differences.

Step-by-Step Solution
• Identify Differences: For the known sequence 102, 104, 107, 113, 128, 173, the differences are:
• 104 - 102 = 2
• 107 - 104 = 3
• 113 - 107 = 6
• 128 - 113 = 15
• 173 - 128 = 45
• Analyze Double Pattern: Look at the ratio of these consecutive differences:
• 3 / 2 = 1.5
• 6 / 3 = 2
• 15 / 6 = 2.5
• 45 / 15 = 3
• The multipliers are increasing by 0.5 (1.5, 2.0, 2.5, 3.0).
• Find (A) and (B): Working backward, the multiplier before 1.5 must be 1.0, and before that 0.5.
• Let the difference between 102 and (B) be d_2. Then d_2 	imes 1 = 2 \Rightarrow d_2 = 2.
• So, 102 - (B) = 2 \Rightarrow (B) = 100.
• Let the difference between (B) and (A) be d_1. Then d_1 	imes 0.5 = 2 \Rightarrow d_1 = 4.
• So, (B) - (A) = 4 \Rightarrow 100 - (A) = 4 \Rightarrow (A) = 96.
• Calculate M: M is 150\% more than (A), meaning M = (A) + 1.5(A) = 2.5 	imes 96 = 240.
• Final Calculation: The difference between M and (B) is 240 - 100 = 140.
• The square root of 140 is approximately 11.83. The nearest integer is 12.

Exam Strategy & Shortcut
When you see numbers growing slowly and then rapidly (like differences jumping from 2 to 45), suspect a multiplicative pattern within the differences. Recognizing this quickly saves time trying additive or exponential patterns.

Common Pitfall
A frequent error is misinterpreting "150% more than (A)" as just "1.5 	imes A". "More than" means you must add it to the original value, making it A + 1.5A = 2.5A.

Final Answer
Therefore, the correct answer is 12.

Question 9

Directions: In the following question, two quantities I and II are given. Compare quantity I and quantity II on its basis. (Only quantity is to be considered).  Two series A and B are given below with one wrong term in series. A: 3, 8, 24, 45, 120, …

Accepted Answer

Concept & Series Pattern Analysis
To evaluate sequence quantities, identify the underlying core mathematical pattern (such as square offsets or prime multipliers) driving the progression, locate the anomalous term in each series, and extrapolate the pattern to find subsequent terms.

Step-by-Step Solution
• Analyze Series A: 3, 8, 24, 45, 120, 168
• Observe the relationship of terms with perfect squares: 3 = 4 - 1 = 2^2 - 1.
• 8 = 9 - 1 = 3^2 - 1.
• 24 = 25 - 1 = 5^2 - 1.
• 120 = 121 - 1 = 11^2 - 1.
• 168 = 169 - 1 = 13^2 - 1.
• The structural pattern is p^2 - 1 where p represents consecutive prime numbers (2, 3, 5, 7, 11, 13).
• For the missing prime p = 7, the term should be 7^2 - 1 = 49 - 1 = 48.
• Therefore, the wrong term in Series A is 45 (it should be 48).
• The next prime in the sequence is 17. The next term of Series A is 17^2 - 1 = 289 - 1 = 288.
• Analyze Series B: 28, 42, 56, 98, 154, 182
• Notice these values are all multiples of 14: 14 	imes 2, 14 	imes 3, 14 	imes 4, 14 	imes 7, 14 	imes 11, 14 	imes 13.
• The base multipliers (2, 3, 7, 11, 13) are consecutive prime numbers, except for the anomalous 4.
• The third multiplier should be the next consecutive prime number, 5. So, the correct term is 14 	imes 5 = 70.
• Therefore, the wrong term in Series B is 56 (it should be 70).
• The next prime multiplier after 13 is 17. The next term of Series B is 14 	imes 17 = 238.
• Evaluate Quantities:
• Quantity I: Average of the wrong terms = \frac{45 + 56}{2} = \frac{101}{2} = 50.5.
• Quantity II: Difference between the computed next terms = 288 - 238 = 50.
• Comparison:
• Quantity I (50.5) > Quantity II (50).

Exam Strategy & Shortcut
Always check for prime number sequences disguised within squares, cubes, or common multipliers. They are frequently used by examiners to break standard arithmetic progression logic and test advanced pattern recognition.

Common Pitfall
Students often mistakenly assume an arithmetic difference sequence (attempting to find second or third differences) and waste valuable time when the true underlying pattern relies on prime numbers. Always test prime squares and prime multiples early.

Final Answer
Therefore, the correct answer is Quantity I > Quantity II.

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