7
Q:

# 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?

 A) 8p B) pq C) pq+27 D) -p

Explanation:

A 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).

Q:

The two given expressions on both the side of the ‘=’ sign will have the same value if two numbers from either side or both side are  interchanged. Select the correct numbers to be interchanged from the given options.

4 + 6 × 7 − 27 ÷ 3 = 7 × 8 − 4 + 39 ÷ 3

 A) 8, 7 B) 6, 8 C) 3,4 D) 6,4

Explanation:

1 611
Q:

Four number-pairs have been given, out of which three are alike in some mannerandoneis different. Select the number-pair that is different.

 A) 16, 8 B) 36, 2 C) 14,8 D) 28, 5

Explanation:

1 508
Q:

What is the smallest integer that is a multiple of 5, 8 and 15?

 A) 600 B) 120 C) 60 D) 40

Explanation:

2 2666
Q:

Which number will fit in '?' place in the following series?

12, 23, 45, 89, ?

 A) 175 B) 176 C) 177 D) 178

Explanation:

7 3418
Q:

Assuming that the numbers in each of the following figures follow a similar pattern, select the option that can replace the question mark (?) in figure C. A) 61 B) 21 C) 16 D) 81

Explanation:

1 881
Q:

The equation of a line is given by 4y-6x+9=0. Find the slope of other line which is perpendicular to it.

 A) -2/3 B) 2/3 C) 3/2 D) -3/2

Explanation:

2 930
Q:

What will be the 20th term in the given sequence?

-50, -47, -44, _

 A) -10 B) 10 C) -7 D) 7

Explanation:

11 3802
Q:

In the given series of numbers how many 7's are there which are immediately followed by 9 and immediately not preceeded by 5 ?

 A) 6 B) 2 C) 1 D) 4