# Problems on Numbers Quiz Set 008

### Question 1

x should be replaced by which minimum number so that 828517x265 is completely divisible by 9?

A

1.

B

2.

C

4.

D

3.

Soln.
Ans: a

If the above number has to be divisible by 9, the sum of the digits, i.e., 8 + 2 + 8 + 5 + 1 + 7 + x + 2 + 6 + 5, should be divisible by 9. So we can see that \$x + 44\$ should be divisible by 9. By inspection, x = 1.

### Question 2

A number is multiplied by 2, then 24 is added to it. The result remains the same if 14 is multiplied to the number and then 240 subtracted. What is the number?

A

22.

B

23.

C

21.

D

24.

Soln.
Ans: a

Let the number be n. From the given conditions we have \$2n + 24 = 14n - 240\$. Rearranging we have \$240 + 24 = 14n - 2n\$, ⇒ \$n = {240 + 24}/{14 - 2}\$. So n = 22.

### Question 3

What is x in \$1{19/x}\$ × \$3{3/8}\$ = \$4{4/5}\$?

A

45.

B

46.

C

44.

D

47.

Soln.
Ans: a

We can see that \$1{19/x}\$ = \${24/5}\$ × \${8/27}\$. ⇒ \${1x + 19}/x\$ = \${64/45}\$ ⇒ x = 45.

### Question 4

If  \$x/7 = y/17 = z/20\$, then \${x + y + z}/x\$ = ?

A

\$6{2/7}\$.

B

\$8{1/2}\$.

C

\$4{1/9}\$.

D

\$7{2/9}\$.

Soln.
Ans: a

Let \$x/7 = y/17 = z/20\$ = k. Then \${x + y + z}/x\$ is same as \${7k + 17k + 20k}/{7k}\$ which equals \$6{2/7}\$.

\${44/7}\$ is same as \$6{2/7}\$.

### Question 5

What is the digit at units place: 1626 × 1947 × 8850?

A

0.

B

1.

C

3.

D

2.

Soln.
Ans: a

The digit at units place = (last digit of 1626) × (last digit of 1947) × (last digit of 8850) = 6 × 7 × 0 = 0, which = 0. 