Sample PSAT Questions---Math3--Grid-ins

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Grid-ins, or student-produced response questions, require you to solve a problem and enter your answer.

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Here are some general hints for answering Student-Produced Response questions, also called Grid-Ins.

Since answer choices aren't given, a calculator may be helpful in avoiding careless mistakes on these questions.


It's suggested that you write your answer in the boxes above the grid to avoid errors in gridding.


The grid can hold only four places and can accommodate only positive numbers and zero.


Do not worry about which column to begin gridding the answer. As long as the answer is gridded completely, you will receive credit.


Unless a problem indicates otherwise, an answer can be entered on the grid either as a decimal or as a fraction.


You don't have to reduce fractions like 3/24 to their lowest terms.


Convert all mixed numbers to improper fractions before gridding the answer.


If the answer is a repeating decimal, you must grid the most accurate value the grid will accommodate.


Some questions may have more than one right answer.


You don't lose any points for a wrong answer.


Know the gridding rules before taking the test.

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You may use a calculator on the math sections.
Students are strongly encouraged to take a calculator to the PSAT/NMSQT, whether or not they plan to use it.

Take a calculator you are comfortable using. Don't buy a new one just for the test.
Don't try to use the calculator on every question. No question requires one.
Decide how to solve each problem before deciding whether to use a calculator.
Practice sample questions with a calculator on hand.

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Approved calculators:

four-function calculator
scientific calculator
graphing calculator

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pocket organizer
hand-held or laptop computer
electronic writing pad or pen input device
calculator with a QWERTY (typewriter-like) keypad
calculator with paper tape
calculator that makes noises or "talks"
calculator that requires an outlet
Students will not be allowed to share calculators with other students.

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question 1 of 7

One out of 5 residents of Central Village was born in that village. If its population is 12,000, what is the total number of its residents who were not born in Central Village?
(from the October 1996 test)

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Correct Answer: 9600

Explanation: One of the first things you should notice about this problem is that you are asked to find the number of residents who were NOT born in Central Village. If 1 out of 5 residents, or 1/5 of the total population, was born in the village, this means that 4 out of 5 residents, or 4/5 of the total population, were not born in the village.

Therefore,

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question 2 of 7


(from the October 14, 1997 test)

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Correct Answer: 300
Explanation:

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question 3 of 7

How many different three-digit numbers between 100 and 1,000 have 5 as the tens digit?
(from the October 18, 1997 test)

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Correct Answer: 90
Explanation: In the 100's, the numbers with 5 as the tens digit are 150, 151, 152, ..., 159 (ten numbers). Also, there will be 10 such numbers in the 200's, in the 300's, etc. Therefore, there are 10*9=90 three-digit numbers between 100 and 1,000 that have 5 as the tens digit.

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question 4 of 7

The measures of the lengths of the three sides of a triangle are prime numbers. If two of the sides are 5 and 23, what is one possible value for the length of the third side?
(from the October 17, 1998 test)

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Correct Answer: 19 or 23
Explanation: Since two of the sides of the triangle are 5 and 23, let y  represent the third side. By the triangle inequality

5 + y  > 23  or  y  > 18
5 + 23 > y   or  y  < 28
23 + y  > 5  or  y  > -18
The lengths of the three sides of the triangle are prime numbers so that y  must be a prime number between 18 and 28. Thus, the two possible values for the length of the third side of the triangle are 19 and 23. Either answer may be gridded as the correct answer to the problem.

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question 5 of 7

The sum of the digits is 6.
Each digit is different.
The number is odd.
What is the greatest 4-digit number that has all of the characteristics listed above?

(from the October 20, 1998 test)

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Correct Answer: 3,201
Explanation: Since the sum of the digits of the four-digit number is 6, none of the digits can be greater than 6. The greatest four-digit number whose digits sum to 6 is 6,000. However, each digit must be different and the number must be odd. The greatest four-digit number having the given characteristics will have the largest digit in the thousands place. To maximize the number in the thousands place, let the units digit be 1. The thousands place cannot be 5 since 5,001 does not have four different digits. The thousands place cannot be 4 since 4,101 still does not have four different digits. If the thousands place is 3, then the number could be 3,201 and this is the greatest four-digit number that satisfies all three given conditions.