Rationale: Using the elimination method the option that fits this description is 26
6-2 = 4 (unit's digit that exceeds its ten's digit by 3)
26*8 = 208 (the product of the given number and the sum of its digits is equal to 175)
The answer: (D)
Question: Which of the options is a two-digit number, which has a unit's digit that exceeds its ten's digit by 4 and the product of the given number and the sum of its digits is equal to 208.
Options:
(A) 15
(B) 37
(C) 55
(D) 26
(E) 73
Reasoning: Here, l = 6 and m = 18
Therefore, first number = l/m x 100% of second number = 6/18 x 100% of second number = 33 1/3% of second number
Ans: (D)
Question: If the given two numbers are respectively 6% and 18% of a third number, then what percentage is the first of the second ?
Options:
(A) 20%
(B) 25%
(C) 18%
(D) 33 1/3%
(E) none of these
Rationale: Money paid in cash = Rs. 1000
Balance payment = (40000 - 1000) = Rs. 39000
The answer: (E)
Question: The price of a T.V. set worth Rs. 40000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Options:
(A) 22678
(B) 26699
(C) 26788
(D) 19000
(E) 39000
Reasoning: We have 3 scenarios here:
1) 1 tech2 businessmen: 4C1 x 5C2 = 40
2) 2 tech1 businessman: 4C2 x 5C1 = 30
3) 3 tech0 businessmen: 4C3 = 4
Total: 144+54+4 = 74
Ans: (A)
Question: An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 5 businessmen, how many possible team submissions are possible?
Options:
(A) 74
(B) 100
(C) 162
(D) 198
(E) 202
Rationale: 216^10 = (6^3)^10 = 6^30
The answer: (E)
Question: What is the greatest positive integer x such that 6^x is a factor of 216^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
Rationale: Speed downstream = d/t = 75/(2 1/2) = 30 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (30 - 18)/2 = 6 kmph
The answer: (B)
Question: A man rows his boat 75 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
(A) 5 kmph
(B) 6 kmph
(C) 9 kmph
(D) 8 kmph
(E) 1 kmph