GATEWAY TO CGL MAINS 2015 : Quant Quiz

Square Root: The square root of a number is a number which multiplied by itself, gives you the original number . Its symbol is called a radical and looks like this: √

For example, 5 x 5 = 25, so the square root of 25 is 5.

Similarly, √ 36 = 6, because 6 x 6 = 36.

Cube Root: The cube root of a number is a value that, when used in a multiplication three times, gives that number.Example: 3 × 3 × 3 = 27, so the cube root of 27 is 3.

Similarly, ∛ 216 = 6, because 6 x 6 x 6 = 216.

Some Questions based on above concept:

5.The digit  in unit’s place of the number (1570)^2 + (1571)^2 + (1572)^2 + (1573)^2 is

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

6.What number must be added to the expression 16a^2 – 12a to make it a perfect square?

(A)  9/4     (B) 11/2    (C) 13/2   (D) 16

7.How many positive integers less than 1000 are multiples of 11 whose square roots are whole numbers.

(A) 2         (B) 4         (C) 8        (D) 11

8.If the number p is 5 more than q and the sum of the squares p and q is 55, then the product of p and q is.

(A) 10      (B) -10       (C) 15       (D) -15

9.The sum of the digits of the smallest number which , when multiplied by 1800, gives a perfect cube, is :

(A) 2       (B) 3            (C) 6        (D) 8

10.The smallest  natural number , by which 3000 must be divided to make the quotient a perfect cube, is :

(A) 3      (B) 4            (C) 5         (D) 6

ANSWER KEY:
1 - (B)
2 - (D)
3 - (A)
4 - (B)
5 - (A)
6 - (A)
7 - (A)
8 - (C)
9 - (C)
10- (A)

SOLUTION:
8.(3) p = q+5
=>p-q = 5
p^2 + q^2 = 55
so (p-q)^2 + 2pq = 55
=>25 + 2 pq = 55
=>2pq = 30
=> pq = 15

9.(3).1800 = 2x2x2x3x3x5x5= 2^3x3^2x5^2
To make 1800 a perfect cube,it must be multiplied by 15(least number)
Required sum = 1+5=6

10 (1) 3000 = 3x1000= 3x10^3

clearly,when we divided 3000 by natural number 3,the quotient is 1000 which is a perfect cube.