question: In the expression 51840/x^4, for which of the following values of x will the expression NOT be an integer?
Options:
(A) 1/2
(B) 1
(C) 2
(D) 3
(E) 5
answer: Stream of consciousness: We can straightaway eliminate A & B, since the expression will always yields an integer for those values
Out of C, D, and E. Let us consider option E. 51840 has only one trailing zero and tens digit is not 5, so It has just one 5 in it. But for the expression to be an integer numerator should have 5^4. The answer is (E).

q: Rs. 5000 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/5:1/5:1/10?
Options:
(A) 1000
(B) 992
(C) 772
(D) 552
(E) 312
a: Stream of consciousness: 1/5:1/5:1/10 = 2:2:1
1/5*5000 = 1000
2000-1000 = 1000 The answer is (A).

question: If x is an odd integer, which of the following is an odd integer?
Options:
(A) 2x+2
(B) x^2
(C) 2x+4x
(D) 1+2x+x^2
(E) 3x-1
answer: Stream of consciousness: Plug in an odd integer; in this case 3
(2*3)+2 = 8 Even
3^2 = 9 Odd
(2*3)+(4*3) = 6 + 12 = 18 Even
1+(2*3)+3^2 = 1+ 6 + 9 = 16 Even
(3*3)-1 = 9 - 1 = 8 Even The answer is (B).

q: There are 47 distinct numbers in set M, there are 28 distinct numbers in set N, and there are 12 distinct numbers that are in both sets M and N. Set H is the set containing the elements that are in at least one of sets M and N. How many elements are in set H?
Options:
(A) 39
(B) 40
(C) 51
(D) 58
(E) 63
a: Stream of consciousness: {Total} = {M} + {N} - {Both}
{Total} = 47 + 28 - 12 = 63. The answer is (E).

question: Dawson earns $100 a week from his job. His income increased and now makes $110 a week. What is the percent increase?
Options:
(A) 5%
(B) 10%
(C) 15%
(D) 20%
(E) 25%
answer: Stream of consciousness: Increase = (10/100)*100 = (1/10)*100 = 10%. The answer is (B).

question: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 54% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
Options:
(A) 60%
(B) 50%
(C) 25%
(D) 19%
(E) 10%
answer:
Stream of consciousness: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 25 + 54 - {both} + 40
{both} = 19%. The answer is (D).