Must or Could be True GMAT, GRE Question

If 4<(7-x)/3, which of the following must be true?

I. 5<x
II. |x+3|>2
III. -(x+5) is positive

A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III

GMAT Remainder Quant Question

How many two-digit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4?

A) One
B) Two
C) Three
D) Four
E) Five

---

If we arrange every 2 digit number then divide by 10 these numbers would all give us remainder 3. So, the number will have 3 in its unit digit : {13 , 23, 33, 43, 53, 63, 73, 83, and 93}

If we divide each number by 4 to see which of them yields reminder 3 then we should see the first number in the set, (13), yields reminder 1. Cross off.

The second number in the set, ( 23), gives us the remainder 3. Keep it.

the third number in the set gives reminder 1. If we continue this then we would see the pattern will be repeated. The even numbers in the set will give a reminder 3

if we count the even numbers that work {23, 43, 63, and 83} then we have 4 numbers

D.

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https://www.cnbc.com/2019/12/11/californias-new-employment-law-is-starting-to-crush-freelancers.html

GMAT, GRE Powers And Integers Quantitative Question

If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w?

A. 26
B. 39
C. 42
D. 65
E. 156

Number Properties GMAT - odds and evens

How many positive even integers less than 100 contain digits 4 or 7?

A. 16
B. 17
C. 18
D. 19
E. 20

---

There are 2 one-digit numbers {4 and 7 }. One of them is even. 

For the two-digit numbers (a and b): 

Numbers that have 4 or 7 for the first digit (4b, 7b).
Since even numbers must end by even digit, b could be {0, 2, 4, 6 or 8}. There are 2 × 5 = 10 such numbers.

Numbers that have 4 as the second digit (a4). These are all even.

The first digit, a, can be anything except 0. So there are 1 × 9 = 9 numbers.

Numbers that have 7 as the second digit (a4, b7) and these are all odd.

Note, that we’ve counted twice the two-digit numbers that have 4 as the second digit and 4 or 7 as the first (44, 74).

Therefore we have 1 + 10 + 9–2 = 18 possible variants overall.

C

GMAT Percent and Interest Question

A t-shirt company charges a flat $50 set-up fee plus $4 per shirt and requires 14 days processing time. For a rush job, the company charges an additional $50 rush set-up fee, plus a surcharge of $1 per shirt per day (in addition to the original amount) for each day less than the standard 14-day processing time. (For instance, 13 days notice would be $5 per shirt, 12 days would be $6 per shirt, etc.)

If a customer orders 50 shirts 5 days prior to his desired pickup date, by what percent is his charge greater than it would have been had he provided at least 14 days’ notice?

A. 180%
B. 200%
C. 210%
D. 280%
E. 300%

---

The cost of purchasing 50 shirts with at least 14 days notice:

50 + 4(50) = 250

In the case of a 5-day notice — 9 days fewer than 14-day notice — each shirt would then be charged $4 + $9 = $13. Then the $50 rush fee would also be added. 

50 + 50 + 13(50) = 100 + 650 = 750

We can now determine the percent change, using the formula percentage Percent change is [(new — old)/old] x 100 percent.

(750–250)/250 x 100

500/250 x 100 = 2 x 100 = 200 percent

B

GMAT Probability Problem -- Ordering Tallest to Shortest

Eight women of eight different heights are to pose for a photo in two rows of four. Each woman in the second row must stand directly behind a shorter woman in the first row. In addition, all of the women in each row must be arranged in order of increasing height from left to right. Assuming that these restrictions are fully adhered to, in how many different ways can the women pose? 

(A) 2
(B) 14
(C) 15
(D) 16
(E) 18

---

There are too many conditions to use a forumla straight away, so let’s work out some options manually. I generally use this approach where a lot of conditions appear in a GMAT question.

Shortest (1) and highest (8) women are fixed:
XXX8
1XXX

2 and 7 have two options, so total 4 patterns:

1:

2xx8
1xx7

|2468| |2568|
|1357| |1347|

2.

2x78
1xxx

|2478| |2578| |2678|
|1356| |1346| |1345|

3.

xxx8
12x7

|4568| |3468| |3568|
|1237| |1257| |1247|

4.

xx78
12xx

|3478| |3678| |3578| |5678| |4578| |4678|
|1256| |1245| |1246| |1234| |1236| |1235| 

14 options.

B

GMAT, GRE Word Problem 600 level

Together, Andrea and Brian weigh p pounds; Brian weighs 10 pounds more than Andrea. Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea. In terms of p, what is Cubby's weight in pounds?

(A) p/2 - 10
(B) 3p/4 - 5
(C) 3p/2 - 5
(D) 5p/4 - 10
(E) 5p - 5

Salary Percent GMAT, GRE Problem

Before a salary hike, the weekly salary of a worker for 40 hours in a week was as much as he is paid now for 35 hours of work in a week. What is the percent increase in his salary for an hour?

A. 11 1/3
B. 12 1/4
C. 13 1/5
D. 14 2/7
E. 15

Probability with rectangles GMAT, GRE

How many unique rectangles are possible that have a perimeter of not more than 258cm and integers for the length of each side?

A. 65
B. 129
C. 4158
D. 4160
E. 130

Arithmetic Progression And Geometric Progression Gmat, Gre Problem

The second, the first and the third term of an Arithmetic Progression  whose common difference is non zero but lesser than 200, form a Geometric Progression in that order. What is the common ration of that Geometric Progression?

A. 1
B. -1+
C. 2
D. -2
E. |1|

Min Max GMAT, GRE Question

Positive integers a, b, c, d and e are such that a < b < c < d < e. If the average (arithmetic mean) of the five numbers is 6 and d - b = 3, then what is the greatest possible range of the five numbers?

A. 12
B. 17
C. 18
D. 19
E. 20

Coordinate Geometry Question GMAT, GRE

The graph of which of the following equations is a straight line that is parallel to line l in the figure above?

(A) 3y − 2x = 0
(B) 3y + 2x = 0
(C) 3y + 2x = 6
(D) 2y − 3x = 6
(E) 2y + 3x = −6

Probability Question GMAT, GRE 650 Level

Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8.

A. 1/12
B. 1/11
C. 1/9
D. 5/36
E. 1/6

Word Problem GMAT, GRE, SAT

The workforce of a certain company comprised exactly 10,500 employees after a four-year period during which it increased every year. During this four-year period, the ratio of the number of workers from one year to the next was always an integer. The ratio of the number of workers after the fourth year to the number of workers after the second year is 6 to 1. The ratio of the number of workers after the third year to the number of workers after the first year is 14 to 1. The ratio of the number of workers after the third year to the number of workers before the four-year period began is 70 to 1. How many employees did the company have after the first year?

(A) 50
(B) 70
(C) 250
(D) 350
(E) 750

Algebraic Inequalities Guide for the GMAT, GRE, SAT

Algebraic Inequalities 

Algebraic inequality statements are solved in the same manner as equations. However, do not forget that whenever you multiply or divide by a negative number, the order of the inequality, that is, the inequality symbol must be reversed. In reading the inequality symbol, remember that it points to the smaller quantity. a < b is read a is less than b. a > b is read a is greater than b.

Example:

Solve for x: 12 – 4x < 8

Solution:

Add –12 to each side.

–4x < –4

Divide by –4, remembering to reverse the inequality sign.x>1

Example:

6x + 5 > 7x + 10

Solution:

Collect all the terms containing x on the left side of the equation and all numerical terms on the right. As with equations, remember that if a term comes from one side of the inequality to the other, that term changes sign.

–x > 5

Divide (or multiply) by –1.x < –5

GMAT, GRE Algebraic problem

Mary and three other students took a math test. Each of their scores was a non-negative integer. The teacher announced that the average score (of the 4 students) was 20. Mary immediately knew that all of the other three students scored below average. What is the minimum score that Mary could have gotten to be certain of the above situation?

A. 40
B. 41
C. 60
D. 61
E. 80

GMAT, GRE Probability Question with Cards

Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is numbered 5?

A. 2/5
B. 3/5
C. 1/18
D. 1/3
E. 1/6

GMAT, GRE Mixture Problem

A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 40% melted chocolate and 60% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each?

A. 1.5
B. 2.5
C. 3
D. 4.5
E. 5

Sequence And Series Gmat, Gre Question

The nth term of a sequence is given by an= 1/n - 1/(n+1) for every positive integer n. What is the sum of the first 100 terms?

(a) 1
(b) 0 
(c) 25
(d) 99/100
(e) 100/101

Repeating Patterns In Decimals Gmat, Gre Problem

What is the 101st digit after the decimal point in the decimal representation of 1/3 + 1/9 + 1/27 + 1/37?

A. 0
B. 1
C. 5
D. 7
E. 8

Gmat Gre Work, Rate, Time

Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 3 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

A. 5
B. 10
C. 15
D. 20
E. 25

Sequence Question GMAT, GRE

A worker is hired for 7 days. Each day, he is paid 10 dollars more than what he is paid for the preceding day of work. The total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days. What was his starting pay?

(A) 90
(B) 138
(C) 153
(D) 160
(E) 163

Group of Groups [ Statistics ] GMAT, GRE

Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 50% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?

A)	60%
B)	50%
C)	25%
D)	15%
E)	10%

Min Max, Critical Value with range GMAT, GRE

How many different values of y$\mathrm{ <span\; face="Tahoma,\; Geneva,\; sans-serif">satisfy</span><span\; face="Tahoma,\; Geneva,\; sans-serif"> </span>}$|y+3|=|8+y|+|4−y|$<span\; face="Tahoma,\; Geneva,\; sans-serif"\; style="font-style:\; inherit;">?</span>$
A. 0
B. 1
C. 2
D. 3
E. 4

Rate Time Distance with [ Ratio ] GMAT, GRE, SAT problem

A contractor undertakes to do a job within 100 days and hires 10 people to do it. After 20 days, he realizes that one fourth of the work is done so he fires 2 people. In how many more days will the work get over?

(A) 60
(B) 70
(C) 75
(D) 80
(E) 100

Hard Exponents Question

Decimal Computation with [ Number Properties ] GMAT, GRE

$\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=$




(A) 10^(-8)
(B) 3*10^(-8)
(C) 3*10^(-4)
(D) 2*10^(-4)
(E) 10^(-4)

Integer Digits [ Combinations ] GMAT, GRE

How many positive integers less than or equal to 2017 contain the digit 0?

(A) 469
(B) 471
(C) 475
(D) 478
(E) 481

3/8 of all students at a school are in all three of the following clubs: Albanian, Bardic, and Chess. 1/2 of all students are in Albanian, 5/8 are in Bardic, and 3/4 are in Chess  If every student is in at least one club, what fraction of the student body is in exactly 2 clubs?

(A) 1/8
(B) 1/4
(C) 3/8
(D) 1/2
(E) 5/8

Simple Interest GMAT, GRE Problem Solving Guide

All interest referred to below is simple interest. The annual amount of interest paid on an investment is found by multiplying the amount invested (the principal) by the percent of interest (the rate).

Example:

Sam invested some of his money in a bank paying 4% interest annually and a second amount, $500 less than the first, in a bank paying 6% interest. If her annual income from both investments was $50, how much money did Sam invest at 6%?

Solution:

As this is a non-ratio algebraic problem, we can handle this with a Distance = Rate x Time chart. Only we'll need an analogy for our names. Let's use: 

PRINCIPAL · RATE = INTEREST INCOME

Let's put it together algebraically.

x = amount invested at 4%x – 500 = amount invested at 6%
.04x = annual interest from 4% investment
.06(x – 500) = annual interest from 6% investment .04x + .06(x – 500) = 50

Multiply by 100 to remove decimals.

4x + 6(x − 500)= 5000 4x + 6x − 3000 = 5000 10x = 8000
x = 800x − 500 = 300

Sam invested $300 at 6%.

Let's try another using our matrix method

Jill invested $7200, part at 4% and the rest at 5%. If the annual income from both investments was the same, find her total annual income from these investments.

1. (A)  $160
2. (B)  $320
3. (C)  $4000
4. (D)  $3200
5. (E)  $1200
   
   

Let x = amount invested at 4%

7200 − x = amount invested at 5% .04x =.05(7200-x)

Multiply by 100 to eliminate decimals.

4x = 5(7200 − x)4x = 36,000 − 5x9x = 36,000
x = 4000
Her income is .04(4000) + .05(3200). 

$320.