Clock

1. An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand
rotate when the clock shows 2 o'clock in the afternoon?

A. 144º B. 150º

C. 168º D. 180º

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2. The reflex angle between the hands of a clock at 10.25 is:
1º
A. 180º B. 192
2

1º
C. 195º D. 197
2

3. A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:

A. 145º B. 150º

C. 155º D. 160º


4. A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same
day, when the watch indicated quarter past 4 o'clock, the true time is:
7
A. 59 min. past 3 B. 4 p.m.
12

7 3
C. 58 min. past 3 D. 2 min. past 4
11 11

5. How much does a watch lose per day, if its hands coincide every 64 minutes?
8 5
A. 32 min. B. 36 min.
11 11

C. 90 min. D. 96 min.

6. At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but,
not together?
2
A. 5 min. past 7 B. 5 min. past 7
11

3 5
11 11

7. At what time between 5.30 and 6 will the hands of a clock be at right angles?
5 7
11 11



8. The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:

A. 0º B. 10º

C. 5º D. 20º


9. At what angle the hands of a clock are inclined at 15 minutes past 5?
1º
A. 58 B. 64º
2

1º 1º
C. 67 D. 72
2 2

10. At 3.40, the hour hand and the minute hand of a clock form an angle of:

A. 120º B. 125º

C. 130º D. 135º

11. How many times are the hands of a clock at right angle in a day?

A. 22 B. 24

C. 44 D. 48


12. The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:

A. 80º B. 75º

C. 60º D. 105º


13. How many times in a day, are the hands of a clock in straight line but opposite in direction?

A. 20 B. 22

C. 24 D. 48


14. At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?


4 6
11 11

15. At what time between 9 and 10 o'clock will the hands of a watch be together?


1 2
11 11
16. At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each
other?
1" 4"
A. 5 B. 12
11 11

4" 4"
C. 13 D. 16
11 11

17. How many times do the hands of a clock coincide in a day?

A. 20 B. 21

C. 22 D. 24


18. How many times in a day, the hands of a clock are straight?

A. 22 B. 24

C. 44 D. 48


19. A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2
p.m. on the following Monday. When was it correct?

A. 2 p.m. on Tuesday B. 2 p.m. on Wednesday

C. 3 p.m. on Thursday D. 1 p.m. on Friday


Problem Solving

Clock Angles

Categories : Problem Solving

Clock based math problems are among the most challenging and interesting problems to
crack.

Basics

For every 60 units that a minute hand move in an hour , the hour hand moves 5 units.

For 12 hours the hour hand completes 360 degrees

1 hour = 360/12 = 30 degrees
60 minutes = 30 degrees
Degrees turned by hour hand in 1 minute = 0.5 degrees

For 1 hour the minute hand completes 360 degrees

1 hour = 360 degrees
60 minutes = 360 degrees
Degrees turned by minute hand in 1 minute = 6 degrees

Lets test what we have learned:

Q) Find the degree between hour hand and minute hand at 3:32'

Hour hand = 3

1 minute ( hour hand) = 0.5 degrees
3 hours = 3*0.5*60(1 hour= 60 minutes)
3 hours ( 3'o clock) = 90 degrees

Minute Hand = 32...
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GMAT Weighted Average - Tutorial and Questions

Categories : Problem Solving

Average Question is an important topic in GMAT problem solving and data sufficiency. Let us
start with the Basics.

Average (Arithmetic Mean)
Average of n numbers a1, a2, a3, a4, a5....an

(An) = (a1+a2+.....an) /n

Example: Find the average of 34, 56, 75 and 83

Answer

a1 = 34
a2= 56
a3=75
a4 = 83

Total Number of Elements (n) = 4

Average (An) = (a1+a2+a3+a4)/n
= (34 + 56 + 75 + 83)/4 = 62

Shortcut to Remember: An x n = a1+a2+.......an

Let us straight away apply this shortcut

Q) The average of four numbers is 20. If one of the numbers is removed, the average of the
remaining numbers is 15. What number was removed?

(A) 10
(B) 15
(C) 30
(D) 35
(E) 45

Answer:

Four Numbers = a1, a2, a3, a4

n=4

An = 20

An x n = a1 + a2 + a3 + a4

20 x 4 = a1 + a2 + a3 + a4 -> Statement 1

Let us assume that a4 has been removed

n=3

15 x 3 = a1 + a2 + a3...
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Top 10 GMAT Problem Solving Tips

Categories : GMAT Tips, Problem Solving

The Problem Solving (PS) section of the GMAT may not be as quirky as the Data Sufficiency
section of the test – but that doesn‘t mean you don‘t need to study for it! PS questions require
more ―straight math‖ than Data Sufficiency questions; in other words, they‘ll probably be more
like the questions you‘re used to seeing on high school and college math tests. The best way to
study? Master the basic concepts from geometry, algebra, statistics, and arithmetic — then
check out these 10 helpful tips!

1. Make sure your fundamentals are strong.

The GMAT doesn‘t allow you to use a calculator—which means you need to be quick and
accurate with basic calculations. Be able to multiply and divide decimals. Know common higher
powers and roots. Have fractions down to a science: Knowing right away whether 3/8 is less
than 5/12 will mean you have more time later to work on more complicated calculations.

2. Choose numbers wisely.

Even questions that don‘t contain variables can still be tackled by choosing numbers wisely.
For example, if a question asks you about ―a multiple of 6,‖ it‘s probably quicker to work with a
particular multiple of 6 (say, 12) than the abstract ―multiple of 6.‖ While studying, identify the
kind of problems where this strategy can be applied.

...
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How to solve work and rates problem in GMAT

Categories : Data Sufficiency, Problem Solving, Rate Problems, Work Problems

Carefully go through the following question types. These are the standard work rate problems
that you would encounter in your GMAT Exam.

Working Together

In questions where individuals work at different speeds, we typically need to add their
separate rates together. Make sure you keep your units straight. This doesn‘t mean wasting
time and writing each and every one out, but rather simply recognizing their existence. Note
that when working together, the total time to complete the same task will be less than BOTH
of the individual rates, but not necessarily in proportion. Nor, are you averaging or adding the
given times taken. You must add rates.

Q) A worker can load 1 full truck in 6 hours. A second worker can load the same truck in 7
hours. If both workers load one truck simultaneously while maintaining their constant rates,
approximately how long, in hours, will it take them to fill 1 truck?

A. 0.15

B. 0.31
C. 2.47
D. 3.23
E. 3.25

The rate of worker #1 is 1 truck/6 hours. This can also be 1/6 trucks/1 hour. The rate of
worker #2 is 1/7. When together, they will complete 1/6 + 1/7 trucks/ 1 hour.

1/6 + 1/7 = 6/42 + 7/42 = 13/42 trucks/1 hour. Remember the question is asking for the
number of hours to fill 1 truck, NOT the number of...
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GMAT Simple Interest and Compound Interest

Categories : Data Sufficiency, Interest Problems, Problem Solving

Simple interest and compound interest - essential topics for an MBA. GMAC thinks the same
too. So you will find these questions randomly distributed in your GMAT Exam.

Simple interest is the most basic and is a function of P, the principle amount of money
invested, the interest rate earned on the principle, i, and the amount of time the money is
invested, t (this is usually stated in periods, such as years or months).

The resulting equation is:

Interest = iPt

In basic terms, the above equation tells us the amount of interest that would be earned on a
principle amount invested (P), for a given time (t) at a given interest rate (i).

Example
If you invested $1,000 (P = your principle) for one year (t = one year) at 6% simple interest (i
= given interest rate), you would get $60 in interest at the end of the year and would have a
total of $1,060.

For compound interest, you would earn slightly more. Let‘s look at similar type problem,
though this one involves compound interest.

Q) Mr. Riley deposits $500 into an account that pays 10% interest, compounded semiannually.
How much money will be in Mr. Riley‘s account at the end...
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Using Venn Diagrams to solve GMAT Set Questions

Categories : Data Sufficiency, Venn Diagrams, Problem Solving, Sets

On your GMAT, you will encounter 1-3 questions that contain overlapping groups with specific
characteristics. You will almost never see more than two characteristics (since you can‘t draw
3D on your scratch paper). For illustration, let‘s take a look at the following Data Sufficiency
example:

Q) Of the 70 children who visited a certain doctor last week, how many had neither a
cold nor a cough?

(1) 40 of the 70 children had a cold but not a cough.
(2) 20 of the 70 children had both a cold and a cough.

There are two characteristics (cough and cold) and two categories for each (yes and no), so
there are four total categories, as indicated by this matrix:

I‘ve filled in the given information from both statements, and the parenthetical information is
inferred. This clearly lays out the 4 combinations of options. If we sum vertically, we can infer
that there are 60 total children with colds. Because there are 70 total children, this also means
that 10 do NOT have colds. The bottom-right quadrant cannot be found because we do not
know how those 10 children get divided between the two empty boxes. Choice E – together the
statements are insufficient...
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Never actually understood Absolute Values ? Here is your chance!

Categories : Absolute Value, Data Sufficiency, Problem Solving

Absolute Values (AVs) questions in GMAT can be a time saver for you if you understand a
few rules. Capture the following notes and use it as a reference for your GMAT exam.

1. Absolute Value equations are two equations disguised as one

You can split up any equation involving absolutes into two, and solve for each solution. One
will look identical to the given, and the other is found by multiplying the inside by -1.

Remember to multiply the entire expression by -1.

| (x + 5)/3 | = 11 turns into:

(x + 5)/3 = 11, and

(x+5)/3 = -11

x + 5 = 33

x + 5 = -33

x = 28 x = -38

Note that plugging either x = 28 or x = -38 into the original equation will check out. Also note
that solutions for variables within absolute value questions can be negative. What is spit out of
the AV cannot be negative, but what goes in can be anything.

2. Think of Absolute Values as distances from zero

If an AV = 15, that means whatever is inside the AV is exactly 15 above or below zero on the
number line.

| x + 5 | = 15

_____-20_____-15_____-10__________0__________+10_____+15_____+20_____

x = -20 and x = 10. Note that this is a SHIFT of -5 from the constant on the...
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GMAT Fractions - Don't get lost in the calculations

Categories : Data Sufficiency, Fractions, Problem Solving

Have you wondered how writers can make a seemingly simple GMAT topic like fractions into
time-consuming calculations. One strategy that GMAT test takers must adopt to simplify the
calculations. For example

Dividing by 5 is the same as multiplying by 2/10. For example:

• 840/5 = ?
• 840/5 = 840*(2/10) = 84*2 = 168

Multiplying or dividing by 10‘s and 2‘s is generally easier than using 5‘s. 90% of the time,
fractions will be easier to perform arithmetic. Decimals are sometimes more useful when
comparing numbers relative to one another, such as in a number line, but these questions are
the exception. Even if given a decimal (or percent) looks easy, quickly convert to a
fraction. Some common ones to memorize:

• 1/9 = 0.111 repeating
• 1/8 = 0.125
• 1/7 = ~0.14

• 1/6 = 0.166 repeating
• 1/5 = 0.20
• 1/4 = 0.25
• 1/3 = 0.333 repeating
• 1/2 = 0.5 repeating

Note: Multiples of these, such as 3/8 (0.375) are also important to remember, but can easily
be derived by multiplying the original fraction (1/8 * 3 = 3/8 = 0.125 * 3 = 0.375)

Denominators are super important. A denominator of a reduced fraction with a multiple of
7 will not have a finite...
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GMAT Solid Geometry - Rectangular Solids and Cylinders

Categories : Data Sufficiency, Problem Solving, Rectangular Solids and Cylinders

Rectangular Solid

Learn the concepts behind volume and surface area before you start solving GMAT Solid
geometry problems. All solid geometry problems come down to this - length, breadth and
height. For data sufficiency questions, look out for values of l, b and h. if any of them are
missing then it would be easy to eliminate answer choices.

6 rectangular faces constitute a rectangular solid

The formulas you need to remember for a rectangular solid are

Volume = Length (l) x Width (w) x Height (h)

Surface Area = (2 x Length x Width) + (2 x Length x Height) + (2 x
Width x Height)

"If length = width = height, that means that the rectangular solid is, in
fact, a cube."

Terminologies

Vertex: Wow! quite a confusing word? Not really

Vertex = Corner

a) Vertex is the number of corners in a...
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How to score well in GMAT Number properties?

Categories : Number Properties, Problem Solving

GMAT Number properties may sound scary, but they just constitute elementary
mathematical principles. You probably know most of these principles by memory; if not, you
could easily execute a calculation to ascertain them. The best option, though, is to study these
principles enough that they seem intuitive. The GMAT Quantitative section is all about saving
time; making number theory second nature will definitely save you some valuable seconds.

1.Odds and Evens

Addition
Even + even = even (12+14=36)
Odd+ Odd = even (13+19=32)
Even + Odd = odd (8 + 11 = 19)

To more easily remember these, just think that a sum is only odd if you add an even and an
odd.
Multiplication

Even x even = even (6 x 4 = 24)
Odd x odd = odd (5 x 3 = 15)
Even x odd = even (6 x 5= 30)

To more easily remember these, just think that a product is only odd if you multiply two odds.

Example Question

If r is even and t is odd, which of the following is odd?

A. rt
B. 5rt
C. 6(r^2)t
D. 5r + 6t
E. 6r + 5t

In this example, we could either plug in numbers for r and t, or we could use our knowledge of
number theory to figure out the...
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Solving GMAT Questions with two linear equations and two unknowns

Categories : Equations, Problem Solving

In order to solve such equations, you need at least 2 distinct equations involving these
unknowns.

For example, if we are trying to solve for x and y, we won't be able to solve it using these 2
equations.

2x + y = 14
4x + y - 14 = 14 - y

Why? Because the two equations on top are the same. If you simplify the second equation,
you get 4x + 2y = 28 which reduces to 2x + y = 14 - the same equation as the first. If the
two equations are the same, then there will be infinitely many values for x and y that will
satisfy the equations. For example, x = 2 and y = 10 satisfies the equation. So does x = 4
and y = 8. And so does x = 6 and y = 2.

In order to solve for an actual value of x and y, we need 2 distinct equations.

For example, if we had

2x + y = 14 --------(1)
x - y = 4 ----------(2)

Then from equation (2), we can get x = 4 + y and substitute that into equation (1) to get:
2(4 + y) + y = 14 We can then solve for y. See if you got y = 2 Once you've got y = 2, you
can substitute that into x= 4 + y to get x = 6.

An important lesson here is that you need as many distinct equations...
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GMAT Word Problems - Basics

Categories : Word Problems, Problem Solving

Word problems on the GMAT get an unfair reputation for being especially challenging.
However, it‘s helpful to think of them as just dressed-up algebra. The real challenge is that
they are (1) long, (2) boring, and (3) require translation from ‗English‘ to ‗Math.‘ Here are a
few questions to ask yourself to make sure you fully break down and understand the problem
BEFORE you start to solve!

What is the problem really asking?

Make sure to understand what the answer choices represent. Are they the total number of
dollars of profit? The profit accumulated by Jenny only? The percent increase in profit from

June to July? Taking the time to do this will also ensure you never leave a problem half
finished. If you dive into setting up an equation too quickly, you may realize half-way through
that you‘re solving for the wrong variable. Sometimes word problems will add an extra step at
the end. You may be busy solving for ―x‖ and forget that the problem is asking for the value of
―1/x‖.

What information am I given?

The best thing about word problems is that they offer information is an organized manner.
Go sentence by sentence, translating any ‗English‘ into ‗Math,‘ looking for the relationship...
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Statistics

Categories : Data Sufficiency, Mean, Median, Mode, Standard Deviation, Descriptive Statistics,Problem
Solving

Even if you fear statistics by its reputation, it is one of the easiest sections in the GMAT
because a standard set of questions is asked and anyone who understands the fundamentals
that I shall describe will be able to ace the questions. The three most basic topics in stats
are mean, mode, and median. Usually, the GMAT will go one step further into range and
standard deviation.

Mean: Mean is the average. Let‘s say there are two numbers: 6 and 8. The mean would be:
(6+8)/2 =14/2 =7. If you analyze the number 7, it makes sense that it is average of 6 and 8.
Using the same approach, the mean of n numbers a1,a2,a3…….an would be
(a1+a2+a3…..+an)/n. If you remember this formula, you should be able to do well with mean
questions. We shall discuss some of the standard questions in subsequent blogs, but for right
now, remember the key formula and start doing some mean and average questions from
Grockit games.

Mode: Let‘s say that you are given a set of numbers, such as {4,3,7,9,9,11,10}. In order to
find the mode, you have to arrange the numbers in ascending order and find the number which
occurs the most. For the set in the example, the ascending order is {3,4,7,9,9,10,11} and 9
occurs the most (two times) and thus is the mode in this...
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Three Types of GMAT Profit and Loss Problems

Categories : Data Sufficiency, Problem Solving, Profit and Loss

You will encounter the following three types of Profit/Loss problems in the GMAT:

Profit/loss as percentage of Cost Price
In this case you will be given the cost price and sales price, and will be asked to simply
calculate the profit/loss incurred by the seller by entering into the given transaction. This will
be done by dividing the difference between the Sales Price and the Cost Price by the Cost
Price. To convert the decimal into a percentage, you will multiply it by 100.

Profit Percentage = ((Sales Price - Cost Price)/Cost Price) x 100

Selling price = Z x (Cost price)

Where Z is any positive number. When Z < 1 we have a loss. When Z = 1 we have neither
profit nor loss. When Z > 1 we have a profit.

Profit or Loss % = (Z - 1) x 100.

Selling price = [(Y / 100) + 1]x (Cost price)

Where Y is the profit or loss percentage. When Y < 0 we have a loss. When Y = 0 we have
neither profit nor loss. When Y > 0 we have a profit.

Profit/loss as percentage of Sales Price
Sometimes the problem will be worded differently and will require the test taker to calculate...
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Area , Perimeter and Circumference

Categories : Data Sufficiency, Geometry Problems, Problem Solving

A sizeable number of GMAT math test questions belong to the Geometry section. Some of
these questions test a candidate‘s ability to understand 2-Dimensional Geometry by asking
the candidate to calculate the area, perimeter or circumference of a geometrical shape.

The following geometrical shapes are most common – Triangles, Quadrilaterals,
Rectangles, Rhombuses, Squares, Circles and Trapeziums.

Triangles – A triangle represents an enclosed shape made by joining three straight lines. The
area of a triangle can be calculated as follows:

Area = ½*Base Side*Height of the triangle

In this formula, the Base Side can be any side of the triangle. However, depending on the base
side chosen, height of the triangle needs to be ascertained. Height of the triangle is the
shortest perpendicular distance from the Base side to the height of the Apex of that triangle.
Note that the height of a triangle may need to be calculated outside the triangle, depending on
the base side chosen.

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