Single Answer Questions:
These questions are multiple-choice questions that asks you to select only one option out of five given options. Normally, these question type will have options written in ovals as shown below:
e.g. If A spends 1/5th of his salary on rent, and 1/6th of the salary on remaining all other expenses. Assuming these two as the only expenses, what fraction of his salary is he saving?
a) 1/3 b) 11/30 c) 19/30 d) 11/15 e) 23/30
Although this question seems to be an easy one, but our objective is to solve it in minimum possible time, so as to spend more time on the tricky questions. A conventional way to solve this question is:
assuming his salary as x,
then he is spending x/5 on rent, and his all other expenditures are x/6
Hence, his savings would be x - (x/5 + x/6) = 19x/30. Therefore, he is saving 19x/30 out of his salary x.
So, the answer is = (19x/30) / x = 19/30.
Our's strategy to solve the same questions is to assume a number for x, which is divisible by 5 and 6 both. Objective is not to have his expenditures into fractions. The best number is the LCM of 5 and 6; i.e. 30.
So, by assuming his salary to be 30, his two expenditures are 6 and 5 respectively. This gives total expenditure as 6 + 5 = 11, therefore total saving = 30 - 11 = 19.
Hence, the answer is, he is saving 19/30 part of his salary.
Important Note: The options will normally give you a hint for a number to start with.You can note that most of the options have 30 in the denominator, which is for salary as per question.
Multiple Answer Questions:
These questions are multiple-choice questions that ask you to select one or more options out of a list of
option. A question may or may not specify the nu_mber of options to select. If the question does not specify how many options to select, select fill that apply.The correct answer may be just one of the options or as many as all of the options, depending on the question. No credit is given unless you select all of the correct
options and no others. And, if the question specifies how many options to select, select exactly that many options.
Usually, these question type will have options written in square boxes as shown below:
e.g. In a coordinate plane, a straight line passes through (-2, -3) and intersects the y-axis above the x-axis. Which of the following could be the slope of this line? [Indicate all such values]
Since, this line intersects the y-axis above origin, say (0, y).Therefore, students would normally solve this question using options as a line passing through (-2, -3) and (0, y) would have slope given in options for positive value of y.This is going to be a challenging task as you would be working with seven different answer choices.
Our's Strategy: The trick is to identify, if this line passes through (-2, -3) and origin (0, O), then it will have a slope of 3/2. But, since this line is intersecting the y-axis above the origin, its slope has to be more than 3/2 (because delta y is more than 3 now, while delta x remains 2).Therefore, mark all the options which are more than 3/2. Hence, the answers for this question are E, F and G.
Questions of this type ask you to compare two quantities: Quantity A and Quantity B, and then determine which of four statements describes the comparison.
A. Quantity A is greater than Quantity B.
B. Quantity B is greater than Quantity A.
C. The Quantities A and B both are equal.
D. We cannot compare the quantities, or the relationship cannot be determined from the information given. '
Comparing the quantities having variables into it:
Students normally compare variables by putting in different numbers, but one can miss out few numbers which may change the result of comparison.
Our's strategy: Whenever we are asked to compare the variables, we suggest you to check for zero, one positive integer greater than 1, one negative integer less than -1,one positive fraction (any number between 0 to 1) and one negative fraction (any number between -1 to 0).
Normally, variable comparison question leads to option D, if we can identify a single number where quantities are equal.
Answer for 1st question is D, as at x = 0 or 1, quantities are equal, and if O<x<1, x2 < x.
Answer for 2nd question is A, as x2 is same on both sides and we are subtracting 1 in quantity B.
Answer for 3rd question is D, as x3 is same on both the sides and if we subtract a positive number quantity A will begreater, and if we subtract a negative number quantity B will be greater. Another short way is, both
the quantities are equal at x = 0.
Comparing the quantities having numbers in any format:
A fair coin has been tossed 5 times.
Students usually solve this question by finding the probabilities of both the events and then compare them, this task is tedious as finding out the probabilities in both the cases is time consum in g. We will have to find all the favorable outcomes, i.e. quantity A will include all the outcomes having exactly 3-heads, exactly
4-heads and outcomes having 5-heads. Similarly quantity B will include all the outcomes having exactly 2-heads, exactly 1-head and outcomes having no heads.
Our's strategy: First of all, the answer for this question can never be D, as both the quantities will have answers between 0 and 1, and if you have numbers in any form into both the quantities, then the quantities can obviously be compared.
Instead of working out the probabilities on both the sides, we can figure out that both the quantities are asking about same favorable cases. Therefore, the answer should be C.
Focus on comparison instead of calculation: In Quantitative Comparison questions, GRE never expects you to do the entire calculation and then compare the quantities. Always believe, there has to be a way to compare the quantities without calculating them.
The conventional way to solve this is to calculate the square roots and then compare the quantities.
Our's strategy: Instead of calculating the square roots, compare the quantities in parts. We can easily compare 7 with sq.rt(50), and sq.rt(80) with 9. You would surely note that both the terms in quantity B are greater,
hence answer should be B. Also, a careful observation tells you that quantity A is somewhat less than 16, while quantity B is slightly more than 16.
Making the quantities same wherever possible and compare them in pieces: GRE normally asks you to compare the quantities that do not look similar at first glance, but if you dig deep into it, you will realize that there are many similarities.
The conventional way to answer this question is to find the sum of all the numbers in given sets using Arithmetic Progression formula.
Our's strategy: Smart work is to identify the common elements in both the sets. You can observe that integers from 12 to 29 are common in both the sets, so their sum will be same into both the quantities. Now just compare the remaining elements in two sets, quantity A will have 9+10+11 remaining, while quantity B will just have 30 remaining. The sum of remaining elements in both the sets are equal, hence answer is C.