Rationale: 8! = 40320
E. 4^10 = 1048576 (40320/1048576) - this is not a factor of 8!
D. 4^8 = 65536 (40320/65536) - this is not a factor of 8!
C. 4^6 = 4096 (40320/4096) - this is not a factor of 8!
B. 4^4 = 256 (40320/256) - this is not a factor of 8!
A. 4^2 = 16 (40320/16) - this is a factor of 8!
The answer: (A)
Question: If n is the greatest positive integer for which 4^n is a factor of 8!, then n =?
Options:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Reasoning: Vowel: E O
Consonants: V R M N T
First letter can be filled in 2 Ways ( As the question states thatfirst letter has to be a vowel)
Fourth letter can be filled in 5 Ways ( As the question states thatthe last letter has to be a consonant)
Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter
Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 5 ways = 200
Ans: (E)
Question: How many 4 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once?
Options:
(A) 21
(B) 42
(C) 120
(D) 600
(E) 200
Rationale: Distance covered by the car = 64 10 = 640 km
\ Speed = 6408 = 80 km/hr
\ Speed gain = 80 64 = 16 km/hr
The answer: (D)
Question: A car finishes a journey in ten hours at the speed of 60 km/hr. If the same distance is to be covered in eight hours how much more speed does the car have to gain?
Options:
(A) 8 km/hr
(B) 10 km/hr
(C) 12 km/hr
(D) 16 km/hr
(E) None of these
Reasoning: Answer = A) Two
Numbers between 10 - 99 giving remainder 3 when divided by 9 = 12, 21, 30, 39, 48, 57, 66, 75, 84, 93
The Numbers giving remainder 2 when divided by 5 = 12, 57 = 2
Ans: (A)
Question: Count the numbers between 10 - 99 which yield a remainder of 3 when divided by 9 and also yield a remainder of 2 when divided by 5?
Options:
(A) Two
(B) Five
(C) Six
(D) Four
(E) One
Rationale: It's a simple geometry problem. Look at the diagram below:
The answer: (E)
Question: Efrida and Frazer who live 15 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?
Options:
(A) 6
(B) 7
(C) 8
(D) 10
(E) 13
Rationale: Correct Answer: (E)
Let's go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn't have to be true consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us x > y. Remember that x < 0, so x = |x|, and y is positive, so |y| = y. Thus x > y is the same statement as |x| > |y|, and (A) must be true.
The answer: (A)
Question: If x>0, y>0, and |x| > |y|, which of the following must be true?
Options:
(A) x > y
(B) y^2 > x^2
(C) x^3 > y^2
(D) x < y
(E) x < y