Practice questions with solutions
Question 1: Quantitative Comparison
x > 0
| Quantity A | Quantity B |
|---|
| (x + 1)² | x² + 1 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined
Solution
Expand Quantity A: (x + 1)² = x² + 2x + 1.
Compare with Quantity B, x² + 1. Quantity A has an extra 2x. Because x > 0, 2x is always positive, so Quantity A is always greater.
Answer: A
Tip
In Quantitative Comparison, check whether the condition (here x > 0) removes the cases that would change the answer. Without it, x = 0 would make the quantities equal and the answer would be D.
Question 2: Multiple choice, number properties
If n is an integer and 99 < n² < 200, how many different values can n have?
A. 2
B. 4
C. 6
D. 8
E. 10
Solution
The squares between 99 and 200 are 100, 121, 144, 169 and 196, so n can be 10, 11, 12, 13 or 14. Since (-n)² is the same as n², n can also be -10, -11, -12, -13 or -14.
5 positive values + 5 negative values = 10.
Answer: E
The trap: forgetting negative integers and looking for 5, which is not even an option.
Question 3: Multiple choice, overlapping sets
In a survey of 500 students, 60% play cricket, 50% play football and 30% play both. What percentage play neither?
A. 10%
B. 20%
C. 30%
D. 40%
E. 50%
Solution
Total = Cricket + Football - Both + Neither
100% = 60% + 50% - 30% + Neither
100% = 80% + Neither
Neither = 20%
The 30% who play both are counted twice when you add 60% and 50%, so you subtract them once.
Answer: B
Question 4: Text Completion
The scientist's reputation for ______ was well earned: every experiment was documented with obsessive precision, and no conclusion was ever advanced without exhaustive supporting data.
A. diligence
B. creativity
C. equivocation
D. prescience
E. ingenuity
Solution
The clues after the colon are "obsessive precision" and "exhaustive supporting data". They describe careful, thorough work.
| Option | Meaning | Fits? |
|---|
| diligence | careful, persistent effort | Yes |
| creativity | original thinking | No clue supports it |
| equivocation | being deliberately vague | The opposite |
| prescience | knowing the future | Not mentioned |
| ingenuity | cleverness in inventing | Not mentioned |
Answer: A
Question 5: Sentence Equivalence
While the politician's public speeches were full of ______ promises, his private memos revealed a far more cautious and practical approach.
Select the two answers that complete the sentence and give it the same meaning.
A. grandiose
B. modest
C. lofty
D. feasible
E. sincere
F. restrained
Solution
"While" signals a contrast with "cautious and practical". The blank needs a word meaning overly ambitious. Grandiose and lofty both mean that, and both give the sentence the same meaning. Modest, feasible and restrained are the opposite. Sincere does not contrast with "cautious".
Answers: A and C
Note
In Sentence Equivalence, both answers must fit the sentence and produce sentences with the same meaning. Two words that each fit but mean different things are wrong.
