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 John or Beth. Carol runs faster than Beth. If both statements are true, the third statement 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 suppose that the first two statements are true. Therefore, we know that John is faster than Carol, which we will denote as (faster 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 (the fastest people are on the left):
J <== F
second <== F
The third statement states that Carol is faster than Beth. Can we reach this conclusion based on the given statements? Can we chain statements together 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 Carol and Beth 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 visual representations adhere to the first two statements, but also show that there is not enough information to come to 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, solves 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 of both events occurring 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 accept your keys.
c) We will not cry or laugh tonight.
d) No errors.
This problem tests a student’s understanding of vocabulary and idioms. In particular, this question tests whether students can identify commonly confused words.
The error in this problem is 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 that means “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 takes 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.