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QUESTION: 1

k is a positive integer. v = 10 × k

Solution:

v = 10 x k ,

Let k = 325 , v = 3250,

The sum of the digits for both remains same which is = (3 + 2 + 5 + 0) = 10

QUESTION: 2

m and n are integers. 0 < m < n < 10

Solution:

When m, n are integers between 1 and 10, and m < n, the number of multiples of m will be more than the number of multiples of n. E.g. for 8 , 9, the number of multiples are respectively 12 and 11

QUESTION: 3

Solution:

The max value of column A is 15 and min is 10,

The max value of column B is 18 and min is 12.

Hence, no relation can be found.

QUESTION: 4

a is a positive integer.

Solution:

When a = 14, the remainder of a and a^{2} are respectively 0 and 0.

But when a = 16, the remainder of a and a^{2} are respectively 2 and 4.

QUESTION: 5

S = (-3, -2, 2, 3). The members of a set T are the squares of numbers in set S.

Solution:

S = { -3 , -2 , 2 ,3 }, T = {9 , 4 }, n ( S ) = 4, n (T ) =2

QUESTION: 6

The average (arithmetic mean) of 5 positive integers is 70.

Solution:

If the integers are (70 ,70 ,70, 70, 70) the median is 70, but if the integers are (60, 65, 65, 80, 80), the median is 65.

QUESTION: 7

R, S and T are 3 consecutive odd integers and R < S < T

Solution:

Since, they are consecutive odd numbers and R < S < T, (S – R) = 2, (T – S) = 2, Adding (S + T) – (R + S) = 4

⇒(S + T) = ( R + S ) + 4,

⇒( S + T ) - 1 = ( R + S ) + 3 > ( R + S ) + 1

QUESTION: 8

x, y and z are negative integers

Solution:

For x = -2, y = -3, z = – 4, x × y × z = -24, x + y + z = -9

But for x = y = z = -1, x × y × z = -1, x + y + z = -3

QUESTION: 9

x is an integer, and the remainder when 2x is divided by 4 is 0

Solution:

If x = 4, 2x = 8, 8 / 4,

the remainder is = 0.

Also for 4/4, the remainder is = 0.

But if x = 6 ,2x = 12 , 12 / 4,

the remainder is = 0. But for 6 / 4 , the remainder is ≠ 0.

QUESTION: 10

Each of w and x is less than 5 and greater than 2. Each of y and z is less than 2 and greater than

Solution:

2 < w < 5, 2 < x < 5.

Adding, we get 4 < ( x + w ) < 10, 1 < y < 2, 1 < z < 2,

Adding, we get 2 < ( y + z ) < 4 < ( w + x ) < 10

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