Reasoning: 11^2 + 13^2 = 121 + 169 = 290
290 - 1 = 289 = 17^2
1 must be subtracted to give a perfect square.
Ans: (A)
Question: The smallest number which when subtracted from the sum of squares of 11 and 13 gives a perfect square is
Options:
(A) 1
(B) 4
(C) 5
(D) 9
(E) 8
Rationale: Left After 1st stroke = 1/2
Left After 2nd stroke = 1/2 * 1/2 = 1/4
Left After 3rd stroke = 1/2 * 1/4 = 1/8
Left After 4th stroke = 1/2 * 1/8 = 1/16
Left After 5th stroke = 1/2 * 1/16 = 1/32
So removed = 1- 1/32 = 31/32
The answer: (A)
Question: If 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 5 strokes ?
Options:
(A) 31/32
(B) 7/8
(C) 1/4
(D) 1/8
(E) 1/16
Reasoning: 8C3 [Select any four] - 6C3 [Select all hard backs] = 36.
Ans: (A)
Question: There are 8 books in a shelf that consist of 2 paperback books and 6 hardback books. If 3 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
Options:
(A) 36
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: 90 * 30/60 = 45 kmph
The answer: (E)
Question: The speed of a train is 90 kmph. What is the distance covered by it in 30 minutes?
Options:
(A) 15
(B) 66
(C) 77
(D) 52
(E) 45
Reasoning: Total number of letters = 8
Using these letters the number of 8 letters words formed is P = 8!.
Ans: (B)
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
Options:
(A) 8
(B) 8!
(C) 7!
(D) 7
(E) 5
Reasoning: (80/100) * 40 (10/100) * 15
32 - 15 = 17
Ans: (E)
Question: How much 80% of 40 is greater than 10% of 15?
Options:
(A) 18
(B) 99
(C) 19
(D) 18
(E) 17