model 1 basic number system Practice Questions Answers Test with Solutions & More Shortcuts

Question : 11

If x, y, z and w be the digits of a number beginning from the left, the number is

a) xyzw

b) wzyx

c) x + 10y + 100z + 1000w

d) $10^3$x + $10^2$y + 10z + w

Answer: (d)

In this problem, the digits of the number from the left are x, y, z and w respectively.

So, x is at thousands places, y is at hundreds of places, z is at tens place and w is at ones place.

Thus, the required number be

= (1000×x) + (100×y) + (10×z) + (1×w)

= (1000x + 100y + 10z + w)

Question : 12

If n and p are both odd numbers, which of the following is an even number?

a) n + p

b) n + p + 1

c) np + 2

d) np

Answer: (a)

Let for example:

n=3 p=5

Option a) 3 + 5 = 8 (even number)

Option b) 3 + 5 + 1 = 9 (odd number)

Option c) 3 x 5 + 2 = 17 (odd number)

Option d) 3 x 5  = 3  (odd number)

Question : 13

For the integer n, if $n^3$ is odd, then which of the following statements are true? I. n is odd. II. $n^2$ is odd. III. $n^2$ is even

a) I only

b) II only

c) I and II only

d) I and III only

Answer: (c)

If n3 is odd

⇒ n is odd and n2 is odd

For example

$n^3$ = 27. Then n = 3 & $n^2$ = 9

∴ I and II are true.

Question : 14

If (n - 1) is an odd number, what are the two other odd numbers nearest to it?

a) n, n-1

b) n, n-2

c) n - 3, n + 1

d) n - 3, n + 5

Answer: (c)

(n – 1) is odd

⇒ (n – 1) – 2 & (n – 1) + 2 are odd.

⇒ (n – 3) and (n + 1) are odd.

Question : 15

Which of the following is always odd?

a) Sum of two odd numbers

b) Difference of two odd numbers

c) Product of two odd numbers

d) None of these

Answer: (c)

Option a) 1 + 3 = 4, 3 + 5 = 8

Option b) 1 - 3 = 2, 3 - 5 = 2

Option c)  1 x 3 = 3,  3 x 5 = 15

∴ Option (C) is Correct.

IMPORTANT quantitative aptitude EXERCISES

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