GMAT MATH - DATA SUFFICIENCY

GMAT MATH - DATA SUFFICIENCY

Question

If r, s, and t are all positive integers, what is the remainder of 3^p/10 if p = qst?

(1) s is even
(2) p = 4t

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.

Solution

Answer B

When a number is divided by 10, the remainder is simply the units digit of that number. For example, 243 divided by 10 has a remainder of 3.

Statement 1 INSUFFICIENT: If s is even, we know that the product qst is even and so is p. Knowing that p is even does not help us with definate value to find the reminder.

Statement 2 is SUFFICIENT: If p = 4t and t is an integer, p must be a multiple of 4. so any possible value for p will be (0,4,8,12...). Since at any point we know a definite value of p we know the value of 3 ^ p. So we can find reminder by dividing it by 10.

GMAT Math - Fractions

GMAT Math - Fractions

Question

When 1/10 of 1/10 of 10,000 is subtracted from 1/10 of 4000, the difference is

(A) 100
(B) 200
(C) 300
(D) 400
(E) 500

Solution

Answer (C)

When you rewrite 1/10 of 1/10 of 10,000 is subtracted from 1/10 of 4000, you get this

(1/10 (4000)) - (1/10 (1/10(10000))
400 - (1/10 (1/10(10000))
Solving the inner fraction first
400 - (1/10 (1000))
400 - 100
=300

GMAT MATH : Word Problem - Geometry

Question

A point on the rim of a circular tire that is rotating in a plane is 6 inches from the center of the rim. What is the distance traveled, in inches, by this point in 10 seconds when the tire turns at the rate of 250 revolutions per minute?

A) 36000π
B) 6000π
C) 3000π
D) 500π
E) 1000π 

 Solution

 Answer D

Area covered by a circle is equal to its circumference, which is calculated by 2πR 
If a point is 6 inches from the center of the rim and it rotates in a circle, then radius (R) of the circle is 6 inches.
So the distance covered by one rotation of the rim is  2 (π) (6) = 12π
Distance cover in one minute; based on the information provided in the Question the rim makes 250 revolutions per minute.
Distance covered in 250 revolutions = 12 (π) (250).
The Question wants us to know how far the rim travels in 10 seconds. This can be calculated by multiplying the total distance traveled by (10/60) (10 seconds of 60 seconds of minute).
   12 (π) (250) (10/60) = 500π

 

 

GMAT Math : Data Sufficiency

GMAT Math : Data Sufficiency 

 Question

 How must is 60 percent of a certain number

Statement 1 : 25 percent of twice the number is equal to half the number.
Statement 2 : 50 percent of the number is 20 less than the number.

A) If statement 1 alone is sufficient to answer the question, but statement 2 alone is not sufficient.
(B) If statement 2 alone is sufficient to answer the question, but statement 1 alone is not sufficient.
(C) If both statements together are needed to answer the question, but neither statement alone is sufficient.
(D) If either statement by itself is sufficient to answer the question.
(E) If not enough facts are given to answer the question.

Solution:

 Answer B

Evaluating Statement 1: 25 percent of twice the number is equal to half the number.

 To determine what is 60 of a certain number (say x), you need to know what the value of that number (x) is. Statement 1 seems to provide that equation to solve for the value of x, but when you read this statement closely it is bogus leads you nowhere.

it states as
2 (0.25x ) = 0.5x
0.5x = 0.5x

You cannot solve for the value of x.

 Evaluating Statement 2: 50 percent of the number is 20 less than the number. 

 The Equation for this statement will be

0.5x = x-20
This implies,
x-0.5x= 20
Solving for 
0.5x =20
x=40

Since we know the value of X we can now find 60 percent of x.
So the correct choice is answer B

GMAT Math Practice - Coordinate Geometry

GMAT Math Practice - Coordinate Geometry 

Question

Line P is described by the equation 3x + 2y - 4 = 0.  Which of the following lines is parallel to P and has the same x-intercept as the line  5x - y + 5 = 0?
a) 6x = -5y + 20
b) -y = (3/2)x +20
c)  -4x - 6y =8
d)  y = -3x - 3
e) - 4y = -6x-12

Solution

 For some reason, many GMAT test takers seem to be confused with such a question and they immediately start by plotting points on the axes.

 You need to know simple rule for parallel lines.

Lines are parallel when they have the same slopes, and the slope is easiest to see when a line is written in slope intercept from y = mx + b.

Converting P to that form we get
y = -3x + 4 or
y = -3x + 4
So the slope of any parallel line will be -3. The second condition is given by the 2nd equation.  Its x-intercept is the x-value where y = 0.

That is 5x - 0 + 5 = 0
5x = -1 so
x = -1 .

For each of the given answer choices, we can start by looking for either a matching slope or x-intercept, and then if it matches one, see if it matches both.

Answer D is y = -3 x - 3.

y = -(3)x -3

Therefore the slope is -3, and parallel to P.  Furthermore, substituting in x = -1.y = -3 x -3

y = 3 - 3 = 0 

So this line also has the desired x intercept.

GMAT Math: Word Problem - Set Theory

GMAT Math: Word Problem - Set Theory

 In a village of hundred households, 75 have at least one DVD player, 80 have at least one cell phone, and 55 have at least one MP3 player. Every village has at least one of these three devices. If X and Y are respectively the greatest and the lowest possible number of households that have all the three of these devices, X-Y is :

A) 65

B) 55

C) 45

D) 35

E) 25

Solution

Answer C

This is a really tricky one, you will encounter this on the actual GMAT if you are doing very good on the GMAT math section. This involves sets.

First we need to figure out what the maximum is. We know it is possible there are 55 with all three, since the 55 MP3 owners is smallest set of the three. (Max = # of MP3)

To calculate the fewest possible, we first need to figure out how many must have all three devices. (max possible - max without all three = minimum with all three).

Of the 80 cell phone owners, 25 cannot have an MP3 player 80 - 55 = 25.

Similarly, 20 of the DVD owners cannot have an MP3 player. 75 - 55 = 20.

If the owners who do not have all three are unique (no overlap), we get the maximum number of owners who do not own an MP3 player, and thus cannot own all three devices.

Max possible - maximum without all three = minimum number of people with all three devices.

55 - 45 = 10

Now we can solve:

55 - 10 = 45.

GMAT Math - Word problem; Geometry

GMAT Math - Word problem; Geometry 

Question

A circle is divided into four sections. If 3 sections constitute 1/4, 2/5, and 3/20 of its total area, what is the fractional value of the area of the 4th section?

a) 1/2

b) 1/3

c)1/4

d)1/5

e)1/6

Solution

For this one, fight the urge to draw out the circle. This isn't really a geometry question, despite the fact that it mentions a circle. It's really just a fraction question.

Add the 3 known sections of the circle's area. To do so, find the lowest common demonimator and add the fractions. 1/4 = 5/20, 2/5 = 8/20 and 3/20 The total fractional value of the 3 sections is 16/20. Therefore, the area of the 4th section must be 1 - 16/20 = 1/5.

You could also backsolve if this one's confusing. Look for the choice that, when added to the three given fractions, equals 1.

Answer is D

How to Prepare for GMAT Math?

How to Prepare for GMAT Math?

For success on the GMAT Math, you will have to have this motto  "I LOVE MATH". If you hate math then learn to fake you mind for a few days. Don't worry it is not at all tough.


May people wonder where to start their GMAT Math preparation. Whether you have a strong background in math or not you will have to work on the following pointers to score high on GMAT math.

1) Build your basic concepts

2) Identify the your weakness / Initial diagnostics

3) Practice and practice

4) Repeat

5) Diagnostics

Build your Basics

No matter how good you are at math, I would suggest buying a GMAT guide and brushing up on all the different kinds of math questions that they might throw at you on test day. I used the "Total GMAT Math, by Jeff Sackmann. This might sound very elementary and obvious, but the fact is that most of us fail to realize and understand what types of math questions they will face come test day. If you have a solid working knowledge of the typical questions, this is the first step in boosting your GMAT quant score. But you need to know what skills of Quant GMAT is going to test you on. So it is very important to focus on the right set of topics.

Identify the your weakness / Initial diagnostics

Once you have brushed up your basics, take a initial diagnostics by taking any free GMAT test and see the areas where you are comfortable and the areas where you are not. Once you know the areas of weaknesses then you can take extra care with more practice.

Practice and Practice

After the diagnostics, you will be able to tell what your strengths and weaknesses are. As far as strengths go, it probably doesn’t make too much sense to keep practicing these types of problems that you are comfortable with. As you go along, start to hone in on the areas that are giving you trouble. Perhaps you can keep a spreadsheet or notes of what types of questions are holding you back.

Repeat

The key here is repetition; just do as many as you can. Soon you will discover a comfort level with once more difficult types of questions and you will be on your way to acing the exam. As you go from question to question during your exam, you will really thank yourself for your efforts.

Diagnostics

It is always good to test your preparedness and check if you have overcome your past weaknesses. Another diagnostic at this stage comes very handy. After every diagnostics fine tune your weaknesses so that you are well prepared for the final examination.

Put in your time and it will pay off. Good luck!!

Question - GMAT Math - Word Problem

Question - GMAT Math - Word Problem

Jimmy invested $20,000 in a mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year and decreased 5 percent during each of the next two years. What is the value of the account today?

(A) $20,750

(B) $20,700

(C) $19855

(D) $20,000

(E) $19,000

Solution

First Year,

10% of $20,000 is 20,000(0.1) = 2,000,

so the value of the account after the first year is 20,000 + 2000 = 22,000.

Second Year,

5% of 22,000 is 22000 (.05) = 1100,

so the value of the account after the second year is 22,000 - 1100 = 20,900

Third Year

5% of 20,900 is 20900 * (.05) 1045,

so the value of the account after the third year is 20900 - 1045 = 19855

choice (C) is the correct answer

GMAT MATH - Geometry Question

Question - GMAT MATH - Geometry Question

Volume of a rectangle

The volume of a rectangular solid is x. If the length and width are each increased by 25% and the height is increased by 300%, what is the volume of the new rectangle formed?

a) x
b) 4x
c) 6x
d) 6.25x
e) 10x

Solution:

Formula for volume of a rectangle = length (ln) * width (b) * height (h)

Given, Volume of rectangle = x

ln*b*h =x

Here we need to understand percentage increase.

For example, if 10 increases by 10% then we calculate it as

10 + (10 *(10/100)) = 10 + 1

Similarly
 25 % length increase = ln + ((25/100)*ln) = ln + 0.25ln = 1.25ln
 25 % width increase = w + ((25/100)*w) = w + 0.25w = 1.25w
200% height increase = h + ((300/100)*h) = h + 3h =4h

New Volume = 1.25ln * 1.25w * 4h
                       = 6.25 (ln*w*h)

If ln*b*h =x;
then 6.25 (ln*b*h) = 6.25x

Correct Answer: D