# numbers aptitude 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, 653×0 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