# Problems on Numbers Quiz Set 019

### Question 1

What is the digit at units place: 7020 × 8374 × 4473?

A

0.

B

1.

C

3.

D

2.

Soln.
Ans: a

The digit at units place = (last digit of 7020) × (last digit of 8374) × (last digit of 4473) = 0 × 4 × 3 = 0, which = 0.

### Question 2

If  \$x/3 = y/17 = z/22\$, then \${x + y + z}/x\$ = ?

A

14.

B

15.

C

13.

D

\$5{2/3}\$.

Soln.
Ans: a

Let \$x/3 = y/17 = z/22\$ = k. Then \${x + y + z}/x\$ is same as \${3k + 17k + 22k}/{3k}\$ which equals 14.

14 is same as 14.

### Question 3

How many prime factors does 34650 have?

A

7.

B

8.

C

6.

D

9.

Soln.
Ans: a

We can see that \$34650 = 2^1 × 3^2 × 5^2 × 7^1 × 11^1\$. The number of prime factors is sum of the powers = 7.

### Question 4

How many prime factors does 67500 have?

A

9.

B

10.

C

8.

D

11.

Soln.
Ans: a

We can see that \$67500 = 2^2 × 3^3 × 5^4\$. The number of prime factors is sum of the powers = 9.

### Question 5

When a two digit number is reversed and added to itself we get 55. The product of the digits of that number is 6. What is the number?

A

32.

B

33.

C

31.

D

34.

Soln.
Ans: a

Let the number be ab. When it is reversed and added to itself we get (10a + b) + (10b + a) = 11 × (a + b). We are given 55 = 11 × (a + b) ⇒ \$a + b = 55 / 11 = 5\$, so the digits are \$a\$ and \$5 - a\$. We are given their product as a × (5 - a) = 6, which is a quadratic expression that can be simplified to \$(a - 3) × (2 - a) = 0\$. So the number could be 32 or 23.