Quantitative - Problems on Numbers plus B64

Quantitative - Problems on Numbers plus B64
Question:-
Option (A)
5
Option (B)
6
Option (C)
7
Option (D)
8
Correct Option:
C
Question Solution:
if it was Rs. 7 then you need 3 bags with Rs. 1 (=20), Rs. 2 (=21) & Rs. 4 (=22) in it. That means you need 3 bags.
Same way if it was Rs. 15 then you need 3 bags with Rs. 1 (=20), Rs. 2 (=21), Rs. 4 (=22) & Rs. 8 (=22) in it. That means you need 4 bags. It will be same for any amount more than Rs. 7 till Rs. 15.
Same way till 31 you need 5 bags, till 63 you need 6 bags, till 127 you need 7 bags & so on.

You can make a general formula for these kind of questions. Calculate lowest n so that 2n n is more than the required number (like 100 here. This n will be the answer.
Question:-
Option (A)
1
Option (B)
2
Option (C)
3
Option (D)
4
Correct Option:
C
Question Solution:
(x2 - y2) = 45 i.e (x - y)(x + y) = 45. The factors of 45 possible are, 15, 3; 9, 5 and 45, 1.
Hence, the numbers are 9 and 6, or 7 and 2 or 23 and 22.
Question:-
Option (A)
21
Option (B)
28
Option (C)
33
Option (D)
50
Correct Option:
D
Question Solution:
Factor out the numerator (4*3)(2*11)(5*7). Now this fraction when divided by p would get an integer only if p cancels out with some of the factors. So now lets try it with different answer choices. Except for the (D) all other choices can be cancelled out. So clearly (D) is the answer.
Question:-
Option (A)
X is always odd
Option (B)
X is always even
Option (C)
X is even only if y is odd
Option (D)
X is odd only if y is even
Correct Option:
B
Question Solution:
If y is even => 6y is even => 7x=420-6y is even. For 7x to be even, x has to be even
If y is odd => 6y is even => 7x=420-6y is even. For 7x to be even, x has to be even

So in any case x has to be even for this equation to be true.
Question:-
Option (A)
865
Option (B)
745
Option (C)
845
Option (D)
945
Correct Option:
B
Question Solution:
The unit's digit will be 1 x 5 = 5(no carry over). The tens digit will be (4x1 + 5x2) = 4(carry over 1).
The hundreds digit will be (3x1 + 4x2 + 5x1) = 6 (1 carry over) + 1(carried over from tens) = 7.
Hence, answer is 745.
You can make a general rule for quick calculation same way like above.