Question: If x is an even integer and y is an odd integer, which of the following is an even integer?
Options:
(A) x+y
(B) x+2y
(C) 3x+y
(D) x+y^2
(E) x+y+2
Ans: (B)
CoT: Plug in an even integer for x; in this case 2
Plug in an odd integer for y; in this case 1
2+1 = 3 Odd
2+(2*1) = 4 Even
(3*2)+1 = 6 + 1 = 7 Odd
2+(1^2) = 2 + 1 = 3 Odd
2+1+2 = 5 Odd
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Question: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 16 seconds. What is the length of the platform in meters?
Options:
(A) 240 meters
(B) 360 meters
(C) 280 meters
(D) 600 meters
(E) Cannot be determined
Ans: (C)
CoT: Speed of the train in metres/sec = 72000/3600 = 20
Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform
Distance travelled by train to cross the man = 16 * 20 = 320 = Length of train
Length of platform = 600 - 320 = 280
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Question: For some integer y, y^2 - 5 is divisible by all of the following EXCEPT
Options:
(A) 29
(B) 30
(C) 31
(D) 38
(E) 41
Ans: (B)
CoT: Hint: y^2-5 (y is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
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