# Numbers Questions

Q:

On dividing 4150 by a certain number , the quotient is 55 and the remainder is 25, the divisor is

Divisor = $\inline \fn_jvn \left [ \frac{Divided-Remainder}{Quotient} \right ]$

= $\inline \fn_jvn \frac{45\times 46}{2}=75$

4496
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).

2 4338
Q:

Which of the following can be used to illustrate that not all prime numbers are odd?

 A) 1 B) 2 C) 3 D) 4

Explanation:

The only even numbers in the list are 2 and 4, but 4 is not a prime. So 2 can be used to illustrate the statement that all primes are not odd.

1 4314
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

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.

3 4243
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

3 3808
Q:

A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?

 A) 30 B) 24 C) 12 D) 8

Explanation:

When the larger cube is cut into smaller cubes, the corner cubes will have paint on three sides. The cubes in the middle of the faces will have paint on only one side, but the cubes cut from the edges will have paint on two sides. In this case, there will be only one cube one each edge (excluding the corners), and since there are 12 edges, there will be 12 cubes with paint on two sides.

1 3739
Q:

3x + y = 19  and x + 3y = 1. Find the value of 2x + 2y

 A) 20 B) 18 C) 11 D) 10

Explanation:

To solve a pair of simultaneous equations such as those given we can add or subtract them.

Adding we get 4x + 4y = 20

Therefore 2x + 2y = 10

0 3090
Q:

If a positive integer n, divided by 5 has a remainder 2, which of the following must be true?

 A) n is odd B) n + 1 cannot be a prime number C) (n + 2) divided by 7 has remainder 2 D) n + 3 is divisible by 5

Answer & Explanation Answer: D) n + 3 is divisible by 5

Explanation:

You can find the integers which when divided by 5 have a remainder 2 by adding 2 to all multiples of 5. So we have n = 7 , 12, 17, 22 etc.

From this series we can see that n does not have to be odd.

Also n + 1 can be a prime because, for example, 12 + 1 = 13

And (n + 2) / 7 has a remainder 2 in some cases but not all.

Remember the question asks us for what MUST be true, and we see that none of the statements are true in all cases. However, adding 3 to any of the values of n will always give a multiple of 5.