Quantitative Aptitude

General Questions

Quantitative Aptitude Exercise Mode

General Questions

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Question 41
(489 + 375)2 - (489 - 375)2 = ?
(489 x 375)

A
144
B
864
C
2
D
4
E
None of these
Correct Answer: Option D
Given Exp. = (a + b)2 - (a - b)2 = 4ab = 4
ab ab
Question 42
The largest 5 digit number exactly divisible by 91 is:

A
99921
B
99918
C
99981
D
99971
E
None of these
Correct Answer: Option B 
Largest 5-digit number = 99999

 91) 99999 (1098
     91
     ---
     899
     819
     ----
      809
      728
      ---
       81
      ---
 
 Required number = (99999 - 81)
                 = 99918.
Question 43
(51 + 52 + 53 + ... + 100) = ?

A
2525
B
2975
C
3225
D
3775
Correct Answer: Option D

This is an A.P. in which a = 51, l = 100 and n = 50.

Sum = n (a + l) = 50 x (51 + 100)   
2 2

= (25 x 151)   = 3775.

Question 44
The smallest 6 digit number exactly divisible by 111 is:

A
111111
B
110011
C
100011
D
110101
E
None of these
Correct Answer: Option C 
The smallest 6-digit number 100000.

 111) 100000 (900
      999
      -----
        100
        ---

 Required number = 100000 + (111 - 100)
                 = 100011.
Question 45
(35423 + 7164 + 41720) - (317 x 89) = ?

A
28213
B
84307
C
50694
D
56094
E
None of these
Correct Answer: Option D 
  35423         317 x 89 = 317 x (90 -1 )
+  7164         = (317 x 90 - 317)
+ 41720         = (28530 - 317)
  -----         = 28213
  84307
- 28213
  -----
  56094
  -----
Question 46
397 x 397 + 104 x 104 + 2 x 397 x 104 = ?

A
250001
B
251001
C
260101
D
261001
Correct Answer: Option B
Given Exp. = (397)2 + (104)2 + 2 x 397 x 104
= (397 + 104)2
= (501)2 = (500 + 1)2
= (5002) + (1)2 + (2 x 500 x 1)
= 250000 + 1 + 1000
= 251001
Question 47

(12 + 22 + 32 + ... + 102) = ?

A
330
B
345
C
365
D
385
Correct Answer: Option D

We know that (12 + 22 + 32 + ... + n2)

= 1 n(n + 1)(2n + 1)
6

Putting n = 10, required sum

= 1 x 10 x 11 x 21 = 385
6

Question 48
What will be remainder when 17200 is divided by 18 ?
A
17
B
16
C
1
D
2
Correct Answer: Option C

When n is even. (xn - an) is completely divisible by (x + a)

 (17200 - 1200) is completely divisible by (17 + 1), i.e., 18.

 (17200 - 1) is completely divisible by 18.

 On dividing 17200 by 18, we get 1 as remainder.

Question 49
(xn - an) is completely divisible by (x - a), when

A
n is any natural number
B
n is an even natural number
C
n is and odd natural number
D
n is prime
Correct Answer: Option A

For every natural number n, (xn - an) is completely divisible by (x - a).

Question 50
A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is:

A
0
B
1
C
2
D
3
Correct Answer: Option D

Let x = 6q + 3.

Then, x2 = (6q + 3)2

= 36q2 + 36q + 9

= 6(6q2 + 6q + 1) + 3

Thus, when x2 is divided by 6, then remainder = 3.

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