3 Examples of HSPT Problems and Solutions

Here are some examples of the types of problems you can expect to see on the HSPT along with their solutions.

VERBAL
John runs faster than Carol. Frank runs slower than either John or Beth. Carol runs faster than Beth. If both statements are true, the third is
(A truth
(B) false
(C) uncertain

This problem is an example of verbal logic. It assesses understanding of how well a student understands how logical statements can be combined to draw conclusions.

The problem tells us to assume that the first two statements are true. Therefore, we know that John is faster than Carol, which we will denote as (fastest people are on the left):

J <== C

We also know that Frank doesn’t run as fast as John or Beth, which we’ll denote as (faster people are on the left):

J <== F
B <== F

The third statement states that Carol is faster than Beth. Can we come to this conclusion based on the statements given? Can we chain statements to show that Carol is, in fact, faster than Beth? Let’s give a visual representation of some possible conclusions we can draw from the given information. Here’s one where we show that Carol and Beth are running at the same speed.

J <== C
J <== B <== F

Here’s one where we show that Carol is faster than Beth.

J <== C
J <===== B <== F

Here’s one where we show that Beth is faster than Carol.

J <=======C
J <== B <== F

All of these visuals adhere to the first two statements, but they also show that there is not enough information to make a definitive conclusion about the relationship between Carol’s speed and Beth’s speed. Therefore, the answer is (C) uncertain.

MATH
Xavier and Yvonne try to solve a problem independently. The probability that Xavier gets a correct answer is 1/4 and the probability that Yvonne gets a correct answer is 5/8. What is the probability that Xavier, but not Yvonne, will solve the problem?
(A) 7/8
(B) 3/8
(C)5/32
(D) 3/32

This is an advanced probability problem that tests the student’s understanding of how to combine probabilities.

When two events are independent, the probability that they both occur together (event A AND event B) is simply P(A) * P(B), where P(A) represents the probability of A and P(B) represents the probability of B. The probability that Xavier will solve the problem is still 1/4, and the probability that Yvonne will NOT solve the problem is 3/8 (which is 1 – 5/8). Therefore, the probability that both events occur together is simply 1/4 * 3/8 = 3/32, which is answer choice (D).

IDIOM
a) No, I can’t help you tonight.
b) Forgot everything accepts your keys.
c) We will neither cry nor laugh tonight.
d) No errors.

This problem tests a student’s understanding of vocabulary and idioms. In particular, this question assesses whether students can identify commonly confused words.

The error in this problem is found in sentence b). The words “accept” and “except” are homophones (sound the same) in English and are often confused as a result. “Accept” is a verb meaning “to take or receive”; “except” is a preposition meaning “but” or “excluding”. In the context of this award, accepting is meaningless. Try replacing the word with the definition:

He forgot everything take his keys.
against
He forgot everything except his keys.

Clearly, the first sentence doesn’t make sense, and the second sentence makes perfect sense. Therefore “accept” is incorrect.