NTS Test Preparation: Discrete Quantitative Questions

Discrete Quantitative Questions

These are standard multiple-choice questions. Most of such questions require you to do some computations and you have to choose exactly one of the available choices based upon those computations. This section will teach you the basic tactics to attempt such questions.

Question format

Each question will consist of a question statement and the choices labeled from A to E. The number of choices may vary from 2 to 5, but exactly one choice will be correct for each question.

How to attempt?

Following are some tactics, which will lead you to the correct answer.

• Whenever you know how to answer a question directly, just do it. The tactics should be used only when you do not know the exact solution, and you just want to eliminate the choices.
• Remember that no problem requires lengthy or difficult computations. If you find yourself doing a lot of complex arithmetic, think again. You may be going in the wrong direction.
• Whenever there is a question with some unknowns (variables), replace them with the appropriate numeric values for ease of calculation.
• When you need to replace variables with values, choose easy-to-use numbers, e.g. the number 100 is appropriate in most percent-related problems and the LCD (least common denominator) is best suited in questions that involve fractions.
• Apply “back-solving” whenever you know what to do to answer the question but you want to avoid doing algebra. To understand this tactic read the following
  example:
  On Monday, a store owner received a shipment of books. On Tuesday, she sold half of them. On Wednesday after two more were sold, she had exactly 2/5 of the books left. How many were in the shipment?
  (A) 10 (B) 20 (C) 30 (D) 40 (E) 50
  now by this tactic:
  Assume that (A) is the correct answer, if so; she must have 3 books on Wednesday. But 2/5 of 10 are 4, so, (A) is incorrect;
  Assume that (B) is the correct answer, if so; she must have 8 books on Wednesday. 2/5 of 20 are 8, so, (B) is the correct choice, and as there may be only one correct choice, there is no need to check for remaining choices.
  This tactic is very helpful when a normal algebraic solution for the problem involves complex or lengthy calculations.
• If you are not sure how to answer the question, do not leave it unanswered. Try to eliminate absurd choices and guess from the remaining ones. Most of the times four of the choices are absurd and your answer is no longer a guess.
  Many things may help you to realize that a particular choice is absurd. Some of them are listed below.
  • The answer must be positive but some of the choices are negative so eliminate all the negative ones.
  • The answer must be even but some of the choices are odd so eliminate all the odd choices.
  • The answer must be less then 100, but some of the choices are greater than 100 (or any other value) so eliminate all choices that are out of range.
  • The answer must be a whole number, but some of the choices are fractions so eliminate all fractions.
  • These are some examples. There may be numerous situations where you can apply this tactic and find the correct answer even if you do not know the right way to solve the problem.

Example questions with solutions

The following are some examples, which will help you to master these types of questions.

Example:

If 25% of 220 equals 5.5% of X, what is X?

(A) 10 (B) 55 (C) 100 (D) 110 (E) 1000

Solution:

Since 5.5% of X equals 25% of 220, X is much greater than 220. So, choices A, B, C, and D are immediately eliminated because these are not larger than 220. And the correct answer is choice E.

(Note: An important point here is that, even if you know how to solve a problem, if you immediately see that four of the five choices are absurd, just pick the remaining choice and move on.)

Example:

Science students choose exactly one of three fields (i.e. medical sciences, engineering sciences and computer sciences). If, in a college, three-fifths of the students choose medical sciences, one-forth of the remaining students take computer sciences, what percent of the students take engineering sciences?

(A) 10 (B) 15 (C) 20 (D) 25 (E) 30

Solution:

The least common denominator of 3/5 and 1/4 is 20, so assume that there are 20 students in that college. Then the number of students choosing medical sciences is 12 (3/4 of 20). Of the remaining 8 students, 2 (1/4 of 8) choose computer sciences. The remaining 6 choose engineering sciences. As 6 is 30% of 20, the answer is E.

Example:

If a school cafeteria needs C cans of soup each week for each student and there are S students, for how many weeks will X cans of soup last?

(A) CX/S (B) XS/C (C) S/CX (D) X/CS (E) CSX

Solution:

Replace C, S and X with three easy to use numbers. Let C=2, S=5 and X=20. Now each student will need 2 cans per week and there are 5 students, so 10 cans are needed per week and 20 cans will last for 2 weeks. Now put these values in choices to find the correct one. The choices A, B, C, D and E become 8, 50, 1/8, 2 and 200 respectively. So the choice D represents the correct answer.