question: If X is the sum of first 40 positive even integers and Y is the sum of first 40 positive odd integers, what is the value of x-y?
Please try to explain your answers
Options:
(A) 0
(B) 25
(C) 40
(D) 75
(E) 100
answer: Stream of consciousness: First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 40 positive even integers minus the sum of first 40 positive odd integers will be 40. The answer is (C).
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question: 30 pens and 75 pencils were purchased for 630. If the average price of a pencil was 2.00, find the average price of a pen.
Options:
(A) 10
(B) 11
(C) 12
(D) 13
(E) 16
answer: Stream of consciousness: Since average price of a pencil = 2
Price of 75 pencils = 150
Price of 30 pens = (630 150) = 480
Average price of a pen = 48060 = 16 The answer is (E).
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question: A certain number when divided by 39 leaves a remainder 20, what is the remainder when the same number is divided by 13?
Options:
(A) 7
(B) 8
(C) 9
(D) 0
(E) 1
answer: Stream of consciousness: 39 + 20 = 59/13 = 7 (Remainder) The answer is (A).
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question: A wheel rotates 15 times every minute and moves 35 cm during each rotation. How many metres does the wheel move in one hour?
Options:
(A) 6 metre
(B) 12 metre
(C) 120 metre
(D) 315 metre
(E) 130 metre
answer:
Stream of consciousness: Number of times wheel moves in 1 hour = 15 * 60 = 900
:. Distance moves = (900 *35) cms = 31500 cms
In metres = 315 metre The answer is (D).
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