## 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