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- Question
A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?
Options- A. 8p
- B. pq
- C. pq+27
- D. -p
- Correct Answer
- pq+27
ExplanationA perfect cube will have prime factors that are in groups of 3; for example 125 has the prime factors 5 x 5 x 5 , and 64 x 125 will also be a cube because its factors will be 4 x 4 x 4 x 5 x 5 x 5
Consider the answer choices in turn.
8 is the cube of 2, and p is a cube, and so the product will also be a cube.
pq will also be a cube as shown above.
pq is a cube and so is 27, but their sum need not be a cube. Consider the case where p =1 and q = 8, the sum of pq and 27 will be 35 which has factors 5 x 7 and is not a cube.
-p will be a cube.
Since the difference between p and q is raised to the power of 6, this expression will be a cube (with cube root = difference squared).
- 1. If n is even, which of the following cannot be odd?
Options- A. n+3
- B. 2n
- C. n+4
- D. 3n Discuss
- 2. Which of the following is not a prime number?
Options- A. 5
- B. 11
- C. 21
- D. 37 Discuss
- 3. 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 Discuss
- 4. How many digits will be there to the right of the decimal point in the product of 85.44 and .08455 ?
Options- A. 7
- B. 5
- C. 4
- D. 6 Discuss
- 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 Discuss
- 6. 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 Discuss
- 7. How many prime numbers exist in 65×359×113 ?
Options- A. 29
- B. 31
- C. 33
- D. 27 Discuss
- 8. 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 Discuss
- 9. If 1/a+1/b+1/c = 1/(a+b+c) where a+b+c not equals '0', abc not equals '0', What is the value of (a+b) (b+c) (a+c) ?
Options- A. 3
- B. 2
- C. 1
- D. 0 Discuss
- 10. Which of the following is a rational number?
Options- A. 0.241
- B. 1.732
- C. 4
- D. All of the above Discuss
Numbers problems
Search Results
Correct Answer: 2n
Explanation:
In case B, odd times even will give even
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.
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
Correct Answer: 6
Explanation:
Sum of decimal places = 7.
Since the last digit to the extreme right will be zero (since 4 x 5 = 20), so there will be 6 significant digits to the right of the decimal point.
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.
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.
Correct Answer: 31
Explanation:
Given
Thus, there are (5 + 5 + 9 + 9 + 3)= 31 prime numbers.
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
Correct Answer: 0
Explanation:
Let assume the value of a,b &c that will satisfy the equation.
so a=1,b=1,c= -1 or a=1,b= -1 &c=1 or a= -1,b=1,c=1
here all three cases satisfy the equation
assume any one a=1,b=1,c= -1
Hence (a+b)(b+c)(c+a)=(1+1)(1-1)(-1+1) = 0
Correct Answer: 4
Explanation:
Any number which can be expressed as a fraction of two integers like P & Q as P/Q where Q is not equal to zero.
Every integer is a rational number since Q can be 1.
Hence, in the given options, 4 can be expressed as a simple fraction as 4/1. And all other options cannot be expressed as fractions.
Hence, 4 is a rational number in the given options.
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