Number Systems.

1.If one-third of one-fourth of a number is 15, then three-tenth of that number is:

A 35

C.45

B.36

D 54

Answer: D

Let the number be X. (1/3)*(1/4)*X=15 so, required number is 54.

2. Three times the first of three consecutive odd integers is 3 more than twice the third.

The third integer is:

A 9

C.13

B.11

D 15

Answer: D

Let the three integers be x, x + 2 and x +

4. Then, 3x = 2(x + 4) + 3, x = 11.

Third integer = x + 4 = 15.

3. The sum of the squares of three numbers is 138, while the sum of their products taken

two at a time is 131. Their sum is:

A 20

C.40

B.30

D None of these

Answer: A

Let the numbers be a, b and c.

Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.

(a + b + c) 2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.

(a + b + c) 2= 20.

4. The number 3456 is divisible by

A 2 B.4 C.8 D. All of the above

Answer: D

5. If 2P4Q is divisible by 8, then minimum value of P+Q is.

A 0

C.22

B.5

D 18

Answer: A

Here last 3 digits must be divisible by 8. Considering minimum value Q can be 0,4,8( cos,

4Q must be multiple of 4) so choose 0 & 0.so number will be 2040,thus P+Q=0.

6. The LCM of fractions 1/3, 5/9, 4/27 is how many times their HCF?

A 180

C.90

B.1/180

D 1/90

Answer: A

LCM(1/3,5/9,4/27)={LCM(1,5,4)/HCF(3,9,27)}=20/3

HCF(1/3,5/9,4/27)={HCF(1,5,4)/LCM(3,9,27)}=1/27 Thus 20/3=X*(1/27) == 180.

7. If A, B, C, D are even numbers and P, Q, R, S are odd numbers, then which of the

following can never be true?

A (a+b)/p=cqr

C.(p+q)=(a+b+c+d)

B.(d+pqr)=(ab+bc)

D (pqrd)=(abcs)

Answer: B.

Cos, even + even=even; even + odd=odd; odd +

odd=even; Even * even=even; even * odd=even; odd *

odd=odd;

Thus B can never be true.