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Aptitude - Numbers

Exercise : Numbers - General Questions
96.
How many terms are there in the G.P. 3, 6, 12, 24, ... , 384 ?
8
9
10
11
7
Answer: Option
Explanation:

Here a = 3 and r = 6 = 2. Let the number of terms be n.
3

Then, tn = 384     arn-1 = 384

3 x 2n - 1 = 384

2n-1 = 128 = 27

n - 1 = 7

n = 8

Number of terms = 8.

97.
If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?
4x + 6y
x + y + 4
9x + 4y
4x - 9y
Answer: Option
Explanation:

By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.

(4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;

(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;

(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;

(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.

98.
9548 + 7314 = 8362 + (?)
8230
8410
8500
8600
None of these
Answer: Option
Explanation:
  9548          16862 = 8362 + x 
+ 7314          x  = 16862 - 8362 
 -----             = 8500 
 16862
 -----
99.
In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient ?
0
12
13
20
Answer: Option
Explanation:

Number = (12 x 35)

Correct Quotient = 420 รท 21 = 20

100.
2 + 22 + 23 + ... + 29 = ?
2044
1022
1056
None of these
Answer: Option
Explanation:

This is a G.P. in which a = 2, r = 22 = 2 and n = 9.
2

Sn = a(rn - 1) = 2 x (29 - 1) = 2 x (512 - 1)   = 2 x 511   = 1022.
(r - 1) (2 - 1)

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