GRE's quantitative comparison section:

• It is very important not to assume anything. Restricting yourself to the given hypothesis is a sure-shot way of avoiding the trap in the question.
• The focus should be on comparison rather than doing big calculations.
• The answer format is a standard one (you may observe it in the practice questions below) and knowing it well saves time in the actual examination.
• The questions in this section are characterized by obvious mathematical traps; hence it is a good idea to re-check and confirm the answer before you register your answer during the test.

1. A bag contains 5 red, 4 white and 6 green marbles. Additionally, John puts ‘x’ number of red marbles and ‘y’ number of white marbles in the bag such that the probability of selecting a red marble becomes .

Column A		Column A
x		y

(A) Column A is greater than Column B.
(B) Column B is greater than Column A.
(C) Both columns are equal.
(D) The relationship between the columns cannot be determined.

Solution:

Total number of marbles in the bag = 5 + 4 + 6 + x + y = 15 + x + y
Number of red marbles = 5 + x

Therefore, =

=> 15 + 3x = 15 + x + y

=> 2x = y => y > x

2.

Column A		Column A
(1234 x 6789) + (1234 x 3209)		(1234 x 9999) – 9998

(A) Column A is greater than Column B.
(B) Column B is greater than Column A.
(C) Both columns are equal.
(D) The relationship between the columns cannot be determined.

Solution:

Column A:
(1234 x 6789) + (1234 x 3209)
= 1234 X (6789 + 3209) = 1234 X 9998
Column B:
(1234 x 9999) – 9998 = 1234 X (9998 + 1) – 9998
= {(1234 X 9998) – (9998 – 1234)} < 1234 X 9998 Answer: (A)

GRE’s Problem Solving Section

The first and the most important consideration is the preparation form.GRE- Problem Solving is 'exhaustive practice'. One must have tried all the kinds of questions possible on problem solving before you get hold of the sample questions given by ETS in the CD that is sent to the registered test takers.

A lot of sources are available online and one such source is online-tests section at http://www.tcyonline.com/. One can take as much as 50 tests on GRE there. Another way is to join various online groups and communities to get the first hand information of the recent questions in GRE.

Following are the important tips that will help you attempt problem solving questions effectively and accurately:

• Always go through the options while reading and formulating the problem. Options always give some hint and save time.
• Try to express the information given in the problem into mathematical expressions.
• Elimination method is the best in most of the problems.
• Never involve in lengthy calculations.
• For questions involving variables, plug in some value for the variables as it is much easier to deal with numeric values rather than variables.

Problem Solving Sample Questions

1. If the ratio of the number of red cars to the number of white cars parked at a parking lot is 3 to 2. By what percentage is the number of red cars more than the number of white cars?

(A) 25% (B) 50% (C) 75% (D) 100% (E) 150%

Sol. Let the number of red cars be 3 and number of white cars be 2.
So, number of red cars = 2 + ½ x 2
i.e. number of red cars is ½ times more than the white cars
So required percentage = 50%
Alternative, required percentage = (3 – 2)/2 × 100 = 50%

Answer is (B)

Tips: It is not necessary to take the number of cars to be 3x and 2x respectively as, the common multiple will not affect the answer.
Whenever you have to calculate ratio or percentage you can simply take the
common multiple to be 1.

2. If p and q are distinct prime numbers, which of the following statements can never be true?
(A) p/q is not an integer (B) (p – 1) q is even
(C) L.C.M of p and q is pq (D) H.C.F. of p and q is 1
(E) pq is prime

Sol: Again, easy way is to take particular value for p and q.
Say p = 2, q = 3
Now if you check the options starting from (A)
You will find that (B) is not true as (2 – 1) 3 = 3 is not even.
So, you might mark answer as (B).
But it is not the correct answer.
The correct answer is (E) as 2 × 3 = 6 is not prime
In such type of questions, remember the key word in the statement i.e can never be true.
It means one of the options is always false independent of the values of p anq q.
So, take another example, p = 3, q = 5.
Now, (B) is true.
But (E) is again false.
So, whenever you solve the question using particular value take all possible value for the variables and also check all the options before marking the answer.

3. Consider the function
P(a) = ,
If P(a) = 6 X 10–5, a is equal to
(A) –8 (B) –5 (C) 0 (D) 5 (E) 8

Sol: P(a) = 6 X 10–5
=> = 6 X 10–5
=> 103 – a = 10–5
=> 3 – a = – 5
=> a = 8

Answer is (D)

You can also check by substituting the values from options. But it will be time consuming.
So, never stick to one approach.

4. A three-digit number ‘xyz’ is such that yz is divisible by 15. For what value of x, xyz will be divisible by 15?

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

Sol: As, yz is divisible by 15, it must be divisible by 3.
So using divisibility rules for 3, y + z must be divisible by 3.
Now, xyz will be divisible by 15
if it is divisible by 3
if x + y + z is divisible by 3.
Since y +z is divisible by 3, so x must be divisible by 3.
Hence Answer is (C)


Short cut:

If you have no ideas of divisibility rules, again it is the time to take particular value, Take yz = 15


Now check from options that only for x = 3, xyz will be divisible by 15.

GRE’s DI

Data interpretation (DI) is an integral part of the GRE Quantitative Reasoning section. It is characterized by questions based on line graphs, bar charts, tables, case-lets and numbers. DI questions evaluate the test takers' ability to interpret the given data one way or the other by forcing him to use mathematical calculations to reach the desired result. The questions are calculation-intensive and hence pose a lot of problems for individuals who cannot calculate and approximate the given data fast.

Experts from TCY recommend the following techniques to counter the DI challenge:

1. Read Directions: The first area to work upon in DI is "directions". Students must spend a little time in the beginning of the test to read the directions and understand the information given in the table/ chart or graph.

2. The catch: There are certain traps in the DI questions which one must understand in order to counter them. These are

i. Units: Never ignore the units given for the variables (in million dollars, in thousands etc.). Sometimes the answer choices are arranged in such a way that there is always a strong possibility to pick up the wrong one if one does not consider units.

ii. Variable: Don't confuse "change in the value of variable (production /sales /profit etc)" with "percentage change in the variable". You must understand that a change in the value is just the difference between the new and old value; on the other hand percentage change is given by %age change = (Ratio of change in value of the variable with the old value) X 100.

3. Calculations: Instead of wasting time in doing lengthy calculations, you must try to solve the questions using approximations.

4. Short cuts: One must use shortcuts to save time while calculating. For instance, here are two most widely used short cuts in DI:

i. Doubling the value of variable is equivalent to an increase of 100 per cent, tripling is equivalent to an increase of 200 per cent, quadrupling to 300 per centand so on.

ii. A% of B = B% of A i.e. 97.6% of 25 is simply one-fourth of 97.6

AWA Strategy

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