# Numbers Aptitude Test Paper 6

26) Find the value of √ (13√(13√(13√(13√(13√(13√(13))))))).

1. √13
2. 169
3. (13)(127/128)
4. 2197

Explanation:
When the process is not up to infinite, use this formula:
N ((2^t)-1 / 2^t), where the N is the digit, and t is the number of times the digit is repeated.
i.e., the number is 13, so we have: 13 ((2^7)-1 / 2^7) =13(127/128)
Hence, the required value is 13(127/128)

27) Find the value of √ (248+ (√52+ (√144))).

1. 4
2. 8
3. 12√2
4. 16

Explanation:
When the numbers are different, then we have to move from right to left direction.
i.e., √144=12, √ (52+12) => √64 = 8
√ (248+8) = √256 = 16
Hence, the required value is 16.

28) √ (1+ (27/169)) =1+x/13, find the value of x.

1. 32
2. 64
3. 1
4. 52

Explanation:
√ (196/169) = 1+x/13
(14/13) -1 = x/13
1/13 =x/13
Hence, x=1

29) (1+1/2)(1+1/3)(1+1/4) ....... (1+1/x) = ?

1. (x+2)/(x+1)
2. (x+2)/(x+3)
3. (x+1)/2
4. (x+1)/3

Explanation:
This type of questions can be solved by a short trick that is the last term numerator, and the first term denominator will be the answer.
i.e., 1+1/2 = 3/2, 1+1/3 = 4/3, 1+1/4 = 5/4, and so on.
(3/2)*(4/3)*(5/4) .... ((x+1)/x) = (½) (x+1)
The first term numerator cancelled by its next term denominator till the end.
In the end, we get (x+1)/2.

30) (1-1/2)(1-1/3)(1-1/4) ....... (1-1/x) = ?

1. x
2. x-1
3. 1/ (x-1)
4. 1/x

Explanation:
This type of question can solve by a sort trick that is the first term numerator, and the last term denominator will be the answer.
i.e., 1-1/2 = 1/2, 1-1/3 = 2/3, 1-1/4 = 3/4 and so on
(1/2)*(2/3)*(3/4) .... ((x-1)/x) = (1) (1/x)
The first term denominator cancelled by its next term numerator till the end.
In the end, we get 1/x.   