Exercise: Numbers

Questions for: Numbers

(12 + 22 + 32 + ... + 102) = ?
A:
330
B:
345
C:
365
D:
385
Answer: 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

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If 1400 x x = 1050. Then, x = ?
A:
1
4
B:
3
5
C:
2
3
D:
3
4
Answer: D
1400 x x = 1050      x = 1050 = 3
1400 4
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What will be remainder when 17200 is divided by 18 ?
A:
17
B:
16
C:
1
D:
2
Answer: C

When n is even. (xn - an) is completely divisibly 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.

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The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ?
A:
12
35
B:
1
35
C:
35
8
D:
7
32
Answer: A

Let the numbers be a and b. Then, a + b = 12 and ab = 35.

a + b = 12          1 + 1 = 12
ab 35 b a 35

Sum of reciprocals of given numbers = 12
35

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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
Answer: 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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