# Problems on Numbers Quiz Set 007

### Question 1

What is the digit at units place: 7575 × 1390 × 9505?

A

0.

B

1.

C

3.

D

2.

Soln.
Ans: a

The digit at units place = (last digit of 7575) × (last digit of 1390) × (last digit of 9505) = 5 × 0 × 5 = 0, which = 0.

### Question 2

The sum of three consecutive odd integer numbers is -2313. The middle among the three is?

A

-771.

B

-770.

C

-768.

D

-769.

Soln.
Ans: a

Let the numbers be 2n - 3, 2n - 1 and 2n + 1. The sum is 3(2n - 1) = 3 x middle. We are given 3 x middle = -2313, ⇒ middle = \$-2313/3\$, i.e., middle = -771.

### Question 3

What is the digit at units place: 2840 × 2492 × 6032?

A

0.

B

1.

C

3.

D

2.

Soln.
Ans: a

The digit at units place = (last digit of 2840) × (last digit of 2492) × (last digit of 6032) = 0 × 2 × 2 = 0, which = 0.

### Question 4

When a two digit number is reversed and added to itself we get 154. The product of the digits of that number is 49. What is the number?

A

77.

B

78.

C

76.

D

79.

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 154 = 11 × (a + b) ⇒ \$a + b = 154 / 11 = 14\$, so the digits are \$a\$ and \$14 - a\$. We are given their product as a × (14 - a) = 49, which is a quadratic expression that can be simplified to \$(a - 7) × (7 - a) = 0\$. So the number could be 77 or 77.

### Question 5

A number is multiplied by 3, then 13 is added to it. The result remains the same if 13 is multiplied to the number and then 67 subtracted. What is the number?

A

8.

B

9.

C

7.

D

10.

Soln.
Ans: a

Let the number be n. From the given conditions we have \$3n + 13 = 13n - 67\$. Rearranging we have \$67 + 13 = 13n - 3n\$, ⇒ \$n = {67 + 13}/{13 - 3}\$. So n = 8. 