Comparison Questions (important for GRE candidates)

The following 5 problems are called quantitative comparison questions. These are very important for GRE candidates. The others can practice to improve their skills. These questions consists of two questions consists of two questions; one in column A and one is column B. You are to compare to two quantities  and decide whether. 

A) The quaantity in column A is greater
B) The quantity in column B is greater
C) The two Quantities are equal
D) The relationship can't be determined from the information given








Problem: 1  Column A: X²                  1<x<3         Column B: 2x
A) ........     B)  .......      C)  ........      D) ......... 
Ans: Here x is any number between 1 & 3 .
Putting x= 2, we get X² = 4, 2x= 4. Hence the two columns are equal. So, options A & B are eliminated. Now let, x=1.1² = 1.21 & 2x=2(1.1)= 2.2 . Hence C is also eliminated. Hence the answer is D .

Problem: 2  Column A: P                                                                                      column B: 8
                                                       p & q are primes and p+q = 12 
  A) ......    B) ......     C) ......    D) ..........
Ans: Since 5& 7 are the only primes whose sum adds up to 12, p is either 5 or 7. In both cases, p is smaller than 8, Hence the answer is B.

Problem: 3      Column A: ab                                                                      Column B: cd
                                                                     a<b<c<d
A) .....      B) ......      C) ......      D) ...... 

Ans: We will try to solve this problem by choosing numbers that satisfy the condition
              a<b<c>d
Let, a=1, b=2, c=4, d=5
:. ab= 2, cd= 20
So, column B is greater, But this doesn't mean that B is the correct answer. However it eliminates A & C.

Now let us try some other numbers.
Let, a= -5, B= -4, c= -3, d=-1
:. ab= 20; cd= 3
Here column A is greater. Hence B can't be the answer. Therefor the answer is D; The relationship can't be determined from the information given.
Notes:  The choice of numbers to plug in to variables is very important. Here are some guideline;
1. The very bes numbers to use first are: 1, 0, -1
2. Often, fractions between 0 & 1 are useful.
3. Occasionally, large numbers such as 10, & 100 may be used.
4. Do not impose any conditions not specifically stated.

Problem 4:       Column A: w+11                                      Column B: w-11
A) .....     B) .....     C) .....     D)  .....
Ans: There is no restriction on w. So we may use any number. But clearly we know that 11> -11. Now adding w to both sides we have w+11>w-11.
Hence, the answer is A i.e. Column A is greater. There is another way of solving this problem. w is any arbitrary number on the number line.

We can see (w+11) is located on the right side of w, & (w-11) is on the left side. Since (w+11), is on the right side of (w-11), so from the property of the number line we may deduce that (w+11)> (w-11).

Posted in: Number System