Wednesday, February 11, 2009
Data Sufficiency - 53
Answer: D
From statement (1): Square root of a number less than 1 is also less than 1 - sufficient
From statement (2): Reciprocal of any number less than 1 is greater than the number - sufficient
Data Sufficiency - 52
1) y/ x > y
2) x^3 > x^2
Answer: B
From statement (1): y/x > y
=> y > xy
=> y(1-x) > 0
y>0 when x is less than 1 or y<0 when x is greater than 1 ---- hence insufficient
From statement (2): x^3 > x^2
=> x^2(x-1) > 0
=> x^2 >0 and x>1
Since x>1, 1/x can not be greater than 1 ---- hence sufficient
Hence B
Monday, January 12, 2009
Data Sufficiency - 51
1). If the selling price per coat had been twice as much, the store's gross profit on the 20 coats would have been 2400
2). If the store selling price per coat had been $2 more, the store's gross profit on the 20 coats would have been 440
Answer: B
Suppose the cost of each coat = x
Suppose sales price = y
=> Total cost = 20x and sales price = 20y
We are required to find the profit: 20(y-x).
From statement 1): It is given that 20(2y-x)=2400
Doesn't helps to find out 20(y-x) --- insufficient
From statement 2): It is given that 20(y+2-x) = 440,
=> 20(y-x) = 400 --- sufficient
Hence B
Problem Solving - 56
A) 2951
B) 8125
C) 15600
D) 15302
E) 18278
Answer: E
Total ways to pick a 3 letter code = 26*26*26 = 26^3
Total ways to pick a 2 letter code = 26*26 = 26^2
Total ways to pick a 1 letter code = 26
Thus total stocks: 26^3 + 26^2 + 26 = 26(26^2 + 26 + 1) = 18278
Tuesday, November 18, 2008
Problem Solving - 55
A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/ 128
Answer: E
RULE: If denominator of a fraction has just the prime factors of 2 or 5 or both it is terminating otherwise not
128 = 2*2*2*2*2*2*2 => has only factors of 2..hence the ans
Problem Solving - 54
(A) 1/(r+2)
(B) 1/2(r+2)
(C) 1/(3r+2)
(D) 1/(r+3)
(E) 1/(2r+3)
Answer: E
Let total income = x
Let saved = y
=> spent = x-y
Total dollars available that he can spend next year = y(1+r)
Given y(1+r) = (x-y)/2
=> y = x/(2r+3)
Fraction (y/x) = 1/(2r+3)
Hence E
Saturday, November 08, 2008
Problem Solving - 53
A) 96
B) 84
C) 80
D) 70
E) 48
Answer: B
Median day = 20+1)/2 = 10.5 th -- money earned was 84
= Average value of 10th and 11th day in the sequence = Median amount of money
Average value of 10th day = 84
Average value of 11th day = 84
Average value of 10th and 11th day = 84 ans
Friday, November 07, 2008
Data Sufficiency - 50
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.
Answer: OA - C
From Statement 1): It is given that 25 percent of the projects at Company Z have 4 or more employees assigned to each project - but we donot know the percentage of projects who have employees less than 4 or in other words we do not have any information about the rest 75% projects ---- hence insufficient
From Statement 2): It is given that 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project - but we donot know the percentage of projects who have employees more than 2 or in other words we do not have any information about the rest 65% projects---- hence insufficient
Taking both the statements together:
25 percent of the projects at Company Z have employees 4 , 5, 6..
35 percent of the projects at Company Z have employees 2, 1, 0
=> 40% of projects have 3 employees = > median value is 3
(1-35)employees -- (36-75)employees -- (76-100)employees
2 or less than 2 ---------3, 3, 3, ------------ 4 or more than 4
Monday, November 03, 2008
Problem Solving - 52
(A) 2.5
(B) 2.4
(C) 2.3
(D) 2.2
(E) 2.1
Answer: A
Total upstream time taken by boat to travel = 90/ (v-3) hrs
Total downstream time taken by boat to travel = 90/ (v+3) hrs
It is given that upstream took half an hour longer than the trip downstream:
=> 90/(v-3) - 90/(v+3) = 1/2
=> [90*(v+3) - 90(v-3)] / [(v^2) -9)] = 1/2
=> 90*[(v+3)-(v-3)] / [(v^2) -9] = 1/2
=> 90*6/ [(v^2) -9] = 1/2
=> v^2 - 9 = 2*90*6
=> v^2 = 2*90*6 + 9 = 2*9*10*6 + 9 = 9(2*10*6+1) = 9(121) = 9*11*11
=> v = 3*11 = 33
We are suppose to calculate = 90/(v+3) = 90/36 = 30/12 = 5/2 = 2.5 ans
Problem Solving - 51
A. 18
B. 20
C. 22
D. 24
E. 26
Answer: B
10 machines, working at same constant rate, take time to complete a job = 16 hrs
thus 1 machine takes time to complete a job = 10 * 16 = 160 hrs
=> 8 machines will take = 160/8 = 20 hrs to complete the job.
Thursday, October 16, 2008
Problem Solving - 50
I. x=0
II. x < 0
III. x > 0
A). none
B). I only
C). III only
D). I and II
E). II and III
Answer: D
Given x = - |x|
We know that |x| >= 0
=> -|x| = x <=0
Thus inequalities represented by I and II