Q: If X is the sum of first 20 positive even integers and Y is the sum of first 20 positive odd integers, what is the value of x-y?
Please try to explain your answers
Options:
(A) 0
(B) 20
(C) 50
(D) 75
(E) 100
A: OK... 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 20 positive even integers minus the sum of first 20 positive odd integers will be 20.
The answer is (B).

Q: X can finish a work in 20 days. Y can finish the same work in 15 days. Yworked for 9 days and left the job. how many days does X alone need to finish the remaining work?
Options:
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
A: OK... Stream of consciousness: Work done by X in 1 day = 1/20
Work done by Y in 1 day = 1/15
Work done by Y in 9 days = 9/15 = 3/5
Remaining work = 1 3/5 = 2/5
Number of days in which X can finish the remaining work = (2/5) / (1/20) = 8
The answer is (D).

Q: If the personal income tax rate is lowered from 38% to 30%, what is the differential savings for a tax payer having an annual income before tax to the tune of $36500?
Options:
(A) $1825
(B) $5000
(C) $3150
(D) $7000
(E) $10000
A: OK... Stream of consciousness: Saving = (38-33)% of 36500 = 1825.
The answer is (A).

Q: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.9880. Find the share of B?
Options:
(A) 2880
(B) 3000
(C) 3018
(D) 3019
(E) 3012
A:
OK... Stream of consciousness: 60*5:36*6:75*3
100: 72: 75
72/247 * 9880 = 2880
The answer is (A).