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

Answer: Option C

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

Answer: Option D

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

Answer: Option B

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

Answer: Option B

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

Answer: Option A

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

Answer: Option C

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

Answer: Option B

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

Answer: Option C

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

Answer: Option B

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

Answer: Option A

Explanation:

106 x 106 - 94 x 94 = (106)2 - (94)2
= (106 + 94)(106 - 94)    [Ref: (a2 - b2) = (a + b)(a - b)]
= (200 x 12)
= 2400.