Q:

Courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.55 ?

A) 1155 B) 1145
C) 1040 D) None
 
Answer & Explanation Answer: B) 1145

Explanation:

The weight will be 250g plus (1.55 - 0.65)/0.10 units of 100g

250 + 900 = 1150

This is the maximum weight that can be sent at that price. But, weights exceeding

250 + 800 will also get charged this amount (that is what the ‘part thereof’ implies).

Hence a package weighing 1145 will be charged $1145

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2 1511
Q:

Which one of the following cannot be the square of a natural number?

A) 32761 B) 42437
C) 81225 D) 20164
 
Answer & Explanation Answer: B) 42437

Explanation:

The square of a natural number never ends in 7.
42437 is not the square of a natural number

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3 1493
Q:

What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?

A) 4 B) 3
C) 2 D) 1
 
Answer & Explanation Answer: C) 2

Explanation:

6)4456(742
42
--------
25
24
-------
16
12
-----
4
------
Required number = (6-4) = 2.

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2 1405
Q:

n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2*n is divided by 4 ?

A) 3 B) 2
C) 1 D) 0
 
Answer & Explanation Answer: B) 2

Explanation:

Let n=4*q + 3. Then, 2*n = 8*q + 6 = 4(2*q + 1) + 2.
Thus when 2*n is divided by 4, the reminder is 2.

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2 1402
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 & Explanation 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).

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