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

Answer:   C) pq+27



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).

Subject: Numbers
Q:

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

 

12, 23, 45, 89, ?

 

A) 175 B) 176
C) 177 D) 178
 
Answer & Explanation Answer: C) 177

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7 2420
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
 
Answer & Explanation Answer: C) 16

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2 490
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
 
Answer & Explanation Answer: A) -2/3

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2 599
Q:

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

 

-50, -47, -44, _

 

A) -10 B) 10
C) -7 D) 7
 
Answer & Explanation Answer: D) 7

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9 2750
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
 
Answer & Explanation Answer: B) 2

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3 789
Q:

The value of 1+22+23+24+...+29 is

A) 255 B) 511
C) 1021 D) 2047
 
Answer & Explanation Answer: C) 1021

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9 1475
Q:

In an arithmetic progression if 13 is the 3rd term, -­47 is the 13th term, then ­-17 is which term?

A) 9 B) 10
C) 7 D) 8
 
Answer & Explanation Answer: D) 8

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5 1226
Q:

What is the value of (81 + 82 + 83 + ......... +130)?

A) 5275 B) 10550
C) 15825 D) 21100
 
Answer & Explanation Answer: A) 5275

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12 1426