31.
On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?
A. 0 B. 1
C. 2 D. 4
Answer & Explanation
Answer: Option D
Explanation:
Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.
x = 5k + 3
x2 = (5k + 3)2
= (25k2 + 30k + 9)
= 5(5k2 + 6k + 1) + 4
On dividing x2 by 5, we get 4 as remainder.
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32.
How many 3-digit numbers are completely divisible 6 ?
A. 149 B. 150
C. 151 D. 166
Answer & Explanation
Answer: Option B
Explanation:
3-digit number divisible by 6 are: 102, 108, 114,… , 996
This is an A.P. in which a = 102, d = 6 and l = 996
Let the number of terms be n. Then tn = 996.
a + (n – 1)d = 996
102 + (n – 1) x 6 = 996
6 x (n – 1) = 894
(n – 1) = 149
n = 150
Number of terms = 150.
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33.
How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?
A. 8 B. 11
C. 12 D. 13
E. None of these
Answer & Explanation
Answer: Option D
Explanation:
Required numbers are 24, 30, 36, 42, …, 96
This is an A.P. in which a = 24, d = 6 and l = 96
Let the number of terms in it be n.
Then tn = 96 a + (n – 1)d = 96
24 + (n – 1) x 6 = 96
(n – 1) x 6 = 72
(n – 1) = 12
n = 13
Required number of numbers = 13.
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34.
How many of the following numbers are divisible by 3 but not by 9 ?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
A. 5 B. 6
C. 7 D. None of these
Answer & Explanation
Answer: Option B
Explanation:
Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s
2133 9 (X)
2343 12 (/)
3474 18 (X)
4131 9 (X)
5286 21 (/)
5340 12 (/)
6336 18 (X)
7347 21 (/)
8115 15 (/)
9276 24 (/)
Required number of numbers = 6.
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35.
(963 + 476)2 + (963 – 476)2 = ?
(963 x 963 + 476 x 476)
A. 1449 B. 497
C. 2 D. 4
E. None of these
Answer & Explanation
Answer: Option C
Explanation:
Given Exp. = (a + b)2 + (a – b)2 = 2(a2 + b2) = 2
(a2 + b2) (a2 + b2)
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36.
How many 3 digit numbers are divisible by 6 in all ?
A. 149 B. 150
C. 151 D. 166
Answer & Explanation
Answer: Option B
Explanation:
Required numbers are 102, 108, 114, … , 996
This is an A.P. in which a = 102, d = 6 and l = 996
Let the number of terms be n. Then,
a + (n – 1)d = 996
102 + (n – 1) x 6 = 996
6 x (n – 1) = 894
(n – 1) = 149
n = 150.
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37.
A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?
A. 10 B. 11
C. 12 D. 15
Answer & Explanation
Answer: Option A
Explanation:
4 a 3 |
9 8 4 } ==> a + 8 = b ==> b – a = 8
13 b 7 |
Also, 13 b7 is divisible by 11 (7 + 3) – (b + 1) = (9 – b)
(9 – b) = 0
b = 9
(b = 9 and a = 1) (a + b) = 10.
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38.
8597 – ? = 7429 – 4358
A. 5426 B. 5706
C. 5526 D. 5476
E. None of these
Answer & Explanation
Answer: Option C
Explanation:
7429 Let 8597 – x = 3071
-4358 Then, x = 8597 – 3071
—- = 5526
3071
—-
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39.
The smallest prime number is:
A. 1 B. 2
C. 3 D. 4
Answer & Explanation
Answer: Option B
Explanation:
The smallest prime number is 2.
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40.
(12345679 x 72) = ?
A. 88888888 B. 888888888
C. 898989898 D. 9999999998
Answer & Explanation
Answer: Option B
Explanation:
12345679 x 72 = 12345679 x (70 +2)
= 12345679 x 70 + 12345679 x 2
= 864197530 + 24691358
= 888888888