Numbers problems
- 1. Find the remainder when 1234 x 1235 x 1237 is divided by 8.
Options- A. 4
- B. 2
- C. 0
- D. 6 Also asked in: CAT, Bank PO
Correct Answer: 6
Explanation:
When we divide 1234 by 8, remainder is 2
When we divide 1235 by 8, remainder is 3
When we divide 1237 by 8, remainder is 5
---> 2 x 3 x 5 = 30
As 30 will not be the remainder because it is greater than 8,
when 30 divided by 8, remainder = 6.
- 2. A six-digit number is formed by repeating a three-digit number; for example, 404404 or 415415 etc. Any number of this form is always exactly divisible by
Options- A. 101
- B. 901
- C. 1001
- D. 789 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 1001
Explanation:
Here by trial and error method, we can obseve that
404404 = 404 x 1001; 415415 = 415 x 1001, etc.
So, any number of this form is divisible by 1001.
- 3. A teacher multiplies 987 by a certain number and obtains 556781 as her answer. If in the answer, both 6 and 7 are wrong but the other digits are correct, then the correct answer will be
Options- A. 553681
- B. 555181
- C. 556581
- D. 555681 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO
Correct Answer: 555681
Explanation:
Given number is 987 = 3 x 7 x 47.
So, required number must be divisible by each one of 3, 7, 47.
None of the numbers in 553681 and 555181 are divisible by 3. While 556581 is not divisible by 7.
Correct answer is 555681.
- 4. What is the right most integer of the expression 65776759 + 54697467 ?
Options- A. 4
- B. 6
- C. 9
- D. 0 Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 9
Explanation:
Last digit for the power of 6 is 6 (always)
Power cycle of 7 is 7, 9, 3, 1.
Now 467/4 gives a remainder of 3
Then the last digit is = 3
Last digit is 6 + 3 = 9.
- 5. A box contains 90 screws each of 100 gms and 100 bolts each of 150 gms. If the entire box weighs 35.5 kg, then the weight of the empty box is ?
Options- A. 10.5 kgs
- B. 12 kgs
- C. 9.6 kgs
- D. 11.5 kgs Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank PO
Correct Answer: 11.5 kgs
Explanation:
Screws weight = 90x100 = 9000gms
bolts weight = 100 x 150 = 15000gms
weight = screws + bolts => 24000 gms =>24 kg
Given entire box weight = 35.5kg
empty box = entire box weight - weight => 35.5kg - 24kg => 11.5kg
so the empty box is 11.5kg.
- 6. A sequence of natural number 2,3,5,6,10. Such that no square and no cube occurs in the term. Find the 300th term of sequence ?
Options- A. 322
- B. 319
- C. 321
- D. 320 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk
Correct Answer: 320
Explanation:
1 to 300 = 300 numbers
squares btwn 1 to 300 = 1,4,9,16,25,36,49.....289 i.e, total 17
cubes = 1,8,27,64,125,216 i.e, 5
now 1 and 64 are common so total numbers that should be removed ( 17+5-2= 20 )
total 20 term removed so 300th term would be 320
- 7. Which of the following is not a prime number?
Options- A. 5
- B. 11
- C. 21
- D. 37 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 21
Explanation:
A prime number is a whole number greater than 1 whose only factors are 1 and itself.
Factors of 5 are 1, 5
Factors of 11 are 1, 11
Factors of 21 are 1, 3, 7, 21
Factors of 37 are 1, 37.
Hence, according to the definition of a prime number, 21 is not a prime number as it has more than two factors.
- 8. What should be the maximum value of B in the following equation? 8A9 ? 6B2 + 4C6 = 723
Options- A. 4
- B. 1
- C. 5
- D. 7 Also asked in: CAT, Bank Clerk
Correct Answer: 7
Explanation:
1 1
8 A 9
+ 4 C 6
- 6 B 2
7 2 3
We may represent the given sum, as shown below:
1 + A + C - B = 12
A + C - B = 11
Now,giving the maximum values to A and C, i.e.
A = 9 and C = 9, we get B = 7.
- 10. There are several peacocks and deers in a cage (with no other types of animals). There are 72 heads and 200 feet inside the cage. How many peacocks are there, and how many deers ?
Options- A. 42 & 24
- B. 38 & 26
- C. 36 & 24
- D. 44 & 28 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: 44 & 28
Explanation:
Let
x = peacocks
y = deers
2x + 4y = 200
x + y = 72
y = 72 - x
2x + 288 - 4x = 200
x = 44 peacocks
y = 28 deers
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