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

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

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

700 Level GMAT PS Question

At a sandwich shop, all sandwiches sell for the same price. If the shop were to decrease the price of each sandwich, it would sell 5 more sandwiches per day its daily revenue would remain constant at $150. How much could a sandwich currently cost?

A. $3
B. $4
C. $5
D. $6
E. $10

GMAT and GRE Min/Max Quant Problem

A company produces baseball cards in equal numbers of regular packs of 16 and deluxe packs of 30. If, on a certain day a company produces 241 cards, what is the smallest number of additional cards the company needs to produce in order to maintain its regular production practice? 

A) 5 
B) 11 
C) 21 
D) 35 
E) 46

Number Properties + Probability GMAT, GRE Quant

If n is an integer from 1 to 96 (inclusive), what is the probability for N being divisible by 8 when N=n*(n+1)*(n+2)

A. 25%
B 50%
C 62.5%
D. 72.5%
E. 75%

---

Let f(n) = n*(n+1)*(n+2)

The product of the three consecutive numbers will be divisible by 8 if the first of the 3 consecutive numbers is even as it prime factors out to at least three 2’s. 

f(2); the function becomes 2*3*4 will be divisible by 8 because 2 is even.
f(52), the function becomes 52*53*54 will be divisible by 8 because 52 is even
f(61), the function becomes 61*62*63 will NOT be divisible by 8 because 61 is odd

However, there is one more case where the function will be divisible by 8 even when the first number of the three consecutive number is odd;
f(7): the function becomes 7*8*9; the middle term 8 is divisible by 8 and thus the entire function becomes divisible by 8.
f(63): the function becomes 63*64*65; the middle term 64 is divisible by 8 and thus the entire function becomes divisible by 8.

Probability = desired/total

How many functions are there;
f(1) = 1*2*3
f(2) = 2*3*4
f(3) = 3*4*5
f(4) = 4*5*6
…
f(95) = 95*96*97
f(96) = 96*97*98

Total = 96

To find the favorable cases; we need to find the count of all even numbers from 1 to 96 and the count of all numbers that are divisible by 8.

Count of even numbers = (96–2)/2+1=47+1=48
Total numbers divisible by 8 = (96–8)/8+1 = 12

Probability=48+1296=6096=0.625=62.5Probability=48+1296=6096=0.625=62.5

C

700 Level GMAT, GRE Divisibility Quant Problem

If n = 14,444, which of the following operations will not yield a number that is divisible by 11?

A) n - 1
B) n + 10
C) n - 100
D) n + 100,000
E) n - 100,000

GMAT, GRE Quant Mixture Problem

How must a grocer mix 4 types of peanuts worth 54 c, 72 c, $1.2 and $1.44 per pound so as to obtain a mixture at 96 cents per pound?

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

Factors GMAT, GRE Problem

How many integers less than 200 will have only 3 factors?


A. 2
B. 4
C. 6
D. 9
E. 12

Geometry GMAT, GRE Problem

The figure above shows three tangent circles (they touch at exactly one point), each with their centers along the same horizontal axis. The biggest circle contains two smaller ones. Of the two smaller circles, the larger one has a radius of 6 inches and the smaller one has a radius of 3 inches. What is the area of the shaded region?

A. 45π
B. 27π
C. 24π
D. 18π
E. 9π

Algebraic Funds GMAT, GRE Algebra Problem

Ms. Morris invested in Fund A and Fund B. The total amount she invested, in both funds combined, was $100,000. In one year, Fund A paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund A. How much did Ms. Morris invest in Fund A?
(A) $32,000
(B) $36,000
(C) $40,000
(D) $42,000
(E) $45,000

Mixture Problem: GMAT, GRE

24 lbs of coffee P and 25 lbs of coffee V are mixed to make coffee X and Y. The ratio of P to V in coffee X is 4 to 1, in Y is 1 to 5. How much of P is contained in the mixture X?


A. 10
B. 20
C. 30
D. 40
D. 45

GMAT Min/Max Problem

If 7(a – 1) = 17(b – 1), and a and b are both positive integers the product of which is greater than 1, then what is the least possible sum of a and b?

A. 2
B. 7
C. 17
D. 24
E. 26

Inequalities Problem Solving: GMAT, GRE

GMAT, GRE MPG Conversion Problem

A car gets 30 miles to the gallon. If it is modified to use a solar panel, it will use only 75 percent as much fuel as it does now. If the fuel tank holds 15 gallons, how many more miles will the car be able to travel, per full tank of fuel, after it has been modified?

A. 112.5
B. 150
C. 337.5
D. 450
E. 500

GRE, GMAT Work Problem with Remainders

Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. If Machine A's speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. How many hours does it currently take Machine A to produce 1 widget on its own?

A. 1/2
B. 2
C. 3
D. 5
E. 6

Chart Word Problem GMAT, GRE Quant

A shoe cobbler charges n dollars to repair a single pair of loafers. Tomorrow, he intends to earn 240 dollars repairing loafers. If he were to reduce his fee per pair by 20 dollars, he would have to repair an additional pair of the loafers to ear the same amount of revenue. How many pair of loafers does he intend to repair tomorrow?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Overlapping Sets, GMAT GRE Question

Each of the items in a box is either a ball or a cube and each item is either red or blue. 72% of the items are cubes and 54% of the items are blue cubes. What percent of the cubes are red?

(A) 18%
(B) 25%
(C) 46%
(D) 50%
(E) 54%

Variables in Answer Choices with Distance Rate Time GMAT Problem

If Susan takes 9 seconds to run y yards, how many minutes will it take her to run x yards at the same rate?