Inequalities with variables (hard). GMAT, GRE

 

GMAT Quant: Work Rate Typists

Two typists undertake to do a job. The second typist begins working one hour after the first. Three hours after the first typist has begun working, there is still (9/20) of work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually?

A. 12 hours and 8 hours
B. 8 hours and 5.6 hours
C. 10 hours and 8 hours
D. 5 hours and 4 hours
E. 4 hours and 8 hours

Mixture Problem with Refresher in answers: GMAT, GRE, SAT

Four-ninths of a drink mix is dye and the rest is pure ugar. When the mix is added to water a gallon of the drink is made that is 7.5% sugar. What percentage of the gallon is dye?

(A) 6
(B) 6.5
(C) 7.5
(D) 8
(E) 24

GMAT Quant Probability: ascending tickets

 A bag contains 50 tickets numbered 1, 2, 3, 4.....50 of which five are drawn at random and are arranged in ascending order of magnitude. Find the probability that third drawn ticket is equal to 30.

a) 551/15134

b) 1/2

c) 551/15379

d) 1/9

e) 1/50

Functions and Ranges: GMAT, GRE Quant Problem

 

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GMAT, GRE Functions and Graphing Question 

In the function above, if f(k) = 2, then which one of the following could be a value of k?

(A) –1
(B) 0
(C) 0.5
(D) 2.5
(E) 4

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f(k)=2
On the graph, that would mean the x is k and the y is2

In the first quadrant when y = 2 the value for x could be from anywhere from roughly 1.75 to 3.5. 

None of the answer choices are ranges but D is within our range. And since the question asks what value “could be” k, that must be the answer. 

D.

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A refresher on finding a range of values with functions:

Number Properties with Profit: GMAT, GRE QUANT

If the selling price of an item is doubled then the profit is tripled. What is the percentage of profit?


A) 50%
B) 100%
C) 150%
D) 200%
E) 250%

Overlapping Sets In An Interesting GMAT, GRE Quant Problem

There are 750 male and female participants in a meeting. Half of the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?

(A) 75
(B) 100
(C) 125
(D) 175
(E) 225

Relative Range Distance Rate Time GMAT, GRE Problem

The distance between Mercury and Earth changes due to the orbits of the planets. When Mercury is at its closest point to Earth, it is 48 million miles away. When Mercury is at its furthest point from Earth, it is 138 million miles away. For a science project, Ruby calculates the maximum and minimum amount of time it would take to travel from Earth to Mercury in a spacecraft traveling 55 miles per hour. Approximately what are the times, in days?

(A) 3,636 and 10,454
(B) 14,545 and 41,818
(C) 36,364 and 104,545
(D) 87,272 and 250,909
(E) 872,727 and 2,509,091

GMAT, GRE Remainder Question with Variable Choices

A refresher on remainders follows the solution. 

When integer b is divided by 13, the remainder is 6. Which of the following cannot be an integer?

A) 13b/52
B) b/26
C) b/17
D) b/12
E) b/6



"When b is divided by 13, if the remainder is 6"
Let's take that to mean the following:
b/13 = q remainder 6
q will be an integer since it's essentially the answer to the equation.

Rearrange, remembering that remainders stay the same number when you multiply by the divisor (which is 13 in this case)
b = 13q + 6

Plug in the answers so we can see which works best.

A) 13b/12

Will 13(13q + 6)/12 equal an integer if we plus in for q? 

Let's say q = 6. 

If q = 6, then 13q + 6 = 84, which is is divisible by 12; hence 13(84)/12 is an integer.

B) b/26

Could (13q + 6)/26 result in an integer for an integer value of q? 

First off, 26 is exactly 2 times 13. So, for any integer value of q, 13q will either be divisible by 26 if q is even or produce a remainder of 13 if q is odd. 

Adding 6 to 13q, the expression will either produce a remainder of 6 or 19, but will never produce a remainder of zero. So, (13q + 6)/26 = b/26 can never equal an integer.

B.

GMAT GRE Probability Problem

Set A: {1, 3, 4, 6, 9, 12, 15}

If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3?

A. 3/14
B. 2/7
C. 9/14
D. 5/7
E. 11/14

GMAT Inequalities Quant Question

If 4x > y and y< 0 then which of the following could be the value of x/y ?

A)0
B)1/4
C)1/2
D)1
E)2

Hard GMAT Mixture and Ratio Quant Problem

<After the problem solution, there is a refresher on ratios if you would like to review it>


How should a grocer mix 4 types of peanuts, worth 54 cents, 72 cents, $1.2,0, and $1.44 respectively per pound, so that the grocer will make a total mixture which is 96 cents per pound?

(A) 8:4:4:7
(B) 24:12:12:50
(C) 4:8:9:4
(D) 16:42:28:10
(E) Cannot be determined

GMAT Probability - Selection from a group

How many randomly assembled people do u need to have a better than 50% probability that at least 1 of them was born in a leap year?

3
9
27
54
81