# Aptitude - Numbers

### Exercise :: Numbers - General Questions

121.

What is the unit digit in the product (365 x 659 x 771)?

 A. 1 B. 2 C. 4 D. 6

Explanation:

Unit digit in 34 = 1 Unit digit in (34)16 = 1 Unit digit in 365 = Unit digit in [ (34)16 x 3 ] = (1 x 3) = 3

Unit digit in 659 = 6

Unit digit in 74 Unit digit in (74)17 is 1.

Unit digit in 771 = Unit digit in [(74)17 x 73] = (1 x 3) = 3 Required digit = Unit digit in (3 x 6 x 3) = 4.

122.

3251 + 587 + 369 - ? = 3007

 A. 1250 B. 1300 C. 1375 D. 1200 E. None of these

Explanation:

``` 3251          Let 4207 - x = 3007
+ 587          Then,  x = 4207 - 3007 = 1200
+ 369
----
4207
----
```

123.

7589 - ? = 3434

 A. 4242 B. 4155 C. 1123 D. 11023 E. None of these

Explanation:

Let 7589 -x = 3434

Then, x = 7589 - 3434 = 4155

124.

217 x 217 + 183 x 183 = ?

 A. 79698 B. 80578 C. 80698 D. 81268

Explanation:

 (217)2 + (183)2 = (200 + 17)2 + (200 - 17)2 = 2 x [(200)2 + (17)2]       [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)] = 2[40000 + 289] = 2 x 40289 = 80578.

125.

The unit digit in the product (784 x 618 x 917 x 463) is:

 A. 2 B. 3 C. 4 D. 5

Explanation:

Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2

126.

If the number 653 xy is divisible by 90, then (x + y) = ?

 A. 2 B. 3 C. 4 D. 6

Explanation:

90 = 10 x 9

Clearly, 653xy is divisible by 10, so y = 0

Now, 653x0 is divisible by 9.

So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4.

Hence, (x + y) = (4 + 0) = 4.

127.

3897 x 999 = ?

 A. 3883203 B. 3893103 C. 3639403 D. 3791203 E. None of these

Explanation:

 3897 x 999 = 3897 x (1000 - 1) = 3897 x 1000 - 3897 x 1 = 3897000 - 3897 = 3893103.

128.

What is the unit digit in 7105 ?

 A. 1 B. 5 C. 7 D. 9

Explanation:

Unit digit in 7105 = Unit digit in [ (74)26 x 7 ]

But, unit digit in (74)26 = 1 Unit digit in 7105 = (1 x 7) = 7

129.

Which of the following numbers will completely divide (461 + 462 + 463 + 464) ?

 A. 3 B. 10 C. 11 D. 13

Explanation:

(461 + 462 + 463 + 464) = 461 x (1 + 4 + 42 + 43) = 461 x 85

= 460 x (4 x 85)

= (460 x 340), which is divisible by 10.

130.

106 x 106 - 94 x 94 = ?

 A. 2400 B. 2000 C. 1904 D. 1906 E. None of these