GMAT prep: Practice Problems
What are the first ten prime numbers? Correct Answer: 2, 3,5, 7, 11, 13, 17, 19, 23, 29
Sum of two primes Correct Answer: All prime numbers are odd, except the number 2. Thus, the sum of
any two primes will be even unless one of those primes is the number 2
If a sum of primes is odd, one of those primes must be the number 2
Counting total factors Correct Answer: If a number has prime factorization a^w x b^y x c^z (where a, b,
and c are all prime), then the number has (w +1)(y + 1)(z + 1) different factors
Perfect squares Correct Answer: 1) All perfect squares have an odd number of total factors, which
always sum up to an odd number
2) Prime factorization of a perfect square contains only even powers of primes
Should vs. Must Correct Answer: Must = binding obligation
Should = moral obligation
Relative pronoun rules Correct Answer: That - if the clause is essential, it must begin with "that" rather
than "which"
Who/whom - must modify people
Which - cannot modify people
Whose - can modify people or things
Which/whom - sometimes follow prepositions
Where - can modify a noun place but cannot modify metaphorical place (condition, situation,
circumstances, arrangement)
When - modify a noun event or time; "in which" can also be used instead of when
Words used for two things vs. three or more Correct Answer: Use between only with two things or
people. Use among when talking about three or more things or people
Is it ok to insert a comma before because? Correct Answer: Acceptable if "because" is a subordinating
conjunction; in that case, it can be separated from a main clause by a comma. If there are two possible
interpretations without including a comma, there needs to be a comma
If "because" is imperative for the rest of the sentence, don't separate it with a comma
Also, do not use "because" after "the reason". Use "the reason" plus "that"
Incorrect: The reason he left is because he was frustrated
Correct: The reason he left is that he was frustrated
Like vs. As Correct Answer: "Like" is used to compare nouns, pronouns, or noun phrases
"As" can be used to compare two clauses
,Right: Like her brother, Ava aced the test
Right: As her brother did, Ava aced the test
Comparative and Superlative Correct Answer: Do not compare an adverb that ends in -ly by changing
the ending to -er
Wrong: He runs quicker than Jacob.
Right: He runs more quickly than Jacob.
Some adverbs that do not end in -ly are made into comparatives by adding -er
Right: He runs faster than Jacob.
Do not use a comparative adjective unless you have a than in the sentence
Wrong: With winter coming, I will have higher energy bills
Right: I will have higher bills than last year
Pronouns Correct Answer: "This" and "These" are never used as standalone pronouns, nor are "that"
and "those"
Idioms for "ability..." and "capability..." Correct Answer: Wrong: ability of doing...
Right: ability to do...
Right: capability of doing...
Compound Subjects Correct Answer: If two nouns disagree in number with an "or" conjunction, use the
noun closest to the verb to determine agreement
Right: Either the manager or the employees take a break
Right: Either the employees or the manager takes a break
Colon rules Correct Answer: What comes before the colon must be able to stand alone as a sentence
You can insert "namely" or "that is" after the colon, and the result would still be acceptable
Right: I love listening to many kinds of music: namely, classical, rock, rap, and pop
Whatever needs explanation should be placed as close to the colon as possible
Worse: Three factors affect the rate of a reaction: concentration...
Better: The rate of a reaction is affected by three factors: concentration...
The clause after the colon must explain what precedes the colon
What to consume during test Correct Answer: During the break after IR, eat something with protein, fat,
and complex carbs. During the break after Quant, drink glucose (coconut water)
What property do all terminating decimals share? Correct Answer: The simplified denominator of the
decimal must contain only 2's and 5's as prime factors. For example, 7/250 is a terminating decimal
, 0.028, as 250 equals to 2 x 5^3. Fraction 3/30 is also a terminating decimal because 3/30 = 1/10 and
denominator 10 = 2 x 5
"view X as Y" or "view X to be Y" ? Correct Answer: view X as Y
Ex: Many financial experts believe policy makers at the Federal Reserve, now *viewing* the economy
*as* balanced between moderate growth and low inflation, are almost certain to leave interest rates
unchanged.
Is "media" singular or plural? Correct Answer: Plural
Equation for the sum of the degree measures of the n interior angles of a polygon Correct Answer:
180(n - 2)
Each of 90 students participated in at least one of three track tryouts: high jump, long jump, and 100-
meter dash. If 20 students participated in the high jump, 40 students in long-jump, and 60 students in
100-meter dash, and if 5 students participated in all three tryouts, how many students participated in
only two of these tryouts? Correct Answer: Let x be the number who participated in exactly 1 of the
tryouts, y be 2 of tryouts, z be 3 of tryouts. Then x + y + z = 90 and x + 2y + 3z = 120. It is given that z = 5,
so x + y = 85 and x + 2y = 105. Thus, y = *20*
Equation for the sum of the first n terms in an arithmetic sequence Correct Answer: (n/2)(A1 + An)
A train traveled from Station A to B at ave speed of 80 km/hr and from Station B to C at ave speed 60
km/hr. If the train didn't stop at Station B, what was the average speed at which the train traveled from
Station A to C?
1) The distance that the train traveled from A to B was 4 times the distance from B to C
2) The amount of time it took the train to travel from A to B was 3 times the amount of time that it took
the train to travel from B to C Correct Answer: *Time = Dist / Speed*
d1/80 is the amt. of time it took to travel from A to B, and d2/60 is the amt. of time it took to travel from
B to C. We want to find average speed from A to C, given by Total Dist / Total Time = (d1 + d2) / ( (d1/80)
+ (d2/60) )
1) gives d1 = 4d2, which plugged into the above yields an answer
2) gives d1/80 = 3(d2/60), or d1 = 4d2, same as above
Each statement alone is sufficient
A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would
take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car
traveling? Correct Answer: Traveling at 75 km/hr, the car takes 1/75 hr to travel 1 km. In seconds, this
equals 3600/75 = 48 seconds. So this car takes 50 seconds to travel 1 km. In hours, this equals 50/3600 =
1/72 hr. Thus, the speed of the car is 72 km/hr
Is x > 10^10?
What are the first ten prime numbers? Correct Answer: 2, 3,5, 7, 11, 13, 17, 19, 23, 29
Sum of two primes Correct Answer: All prime numbers are odd, except the number 2. Thus, the sum of
any two primes will be even unless one of those primes is the number 2
If a sum of primes is odd, one of those primes must be the number 2
Counting total factors Correct Answer: If a number has prime factorization a^w x b^y x c^z (where a, b,
and c are all prime), then the number has (w +1)(y + 1)(z + 1) different factors
Perfect squares Correct Answer: 1) All perfect squares have an odd number of total factors, which
always sum up to an odd number
2) Prime factorization of a perfect square contains only even powers of primes
Should vs. Must Correct Answer: Must = binding obligation
Should = moral obligation
Relative pronoun rules Correct Answer: That - if the clause is essential, it must begin with "that" rather
than "which"
Who/whom - must modify people
Which - cannot modify people
Whose - can modify people or things
Which/whom - sometimes follow prepositions
Where - can modify a noun place but cannot modify metaphorical place (condition, situation,
circumstances, arrangement)
When - modify a noun event or time; "in which" can also be used instead of when
Words used for two things vs. three or more Correct Answer: Use between only with two things or
people. Use among when talking about three or more things or people
Is it ok to insert a comma before because? Correct Answer: Acceptable if "because" is a subordinating
conjunction; in that case, it can be separated from a main clause by a comma. If there are two possible
interpretations without including a comma, there needs to be a comma
If "because" is imperative for the rest of the sentence, don't separate it with a comma
Also, do not use "because" after "the reason". Use "the reason" plus "that"
Incorrect: The reason he left is because he was frustrated
Correct: The reason he left is that he was frustrated
Like vs. As Correct Answer: "Like" is used to compare nouns, pronouns, or noun phrases
"As" can be used to compare two clauses
,Right: Like her brother, Ava aced the test
Right: As her brother did, Ava aced the test
Comparative and Superlative Correct Answer: Do not compare an adverb that ends in -ly by changing
the ending to -er
Wrong: He runs quicker than Jacob.
Right: He runs more quickly than Jacob.
Some adverbs that do not end in -ly are made into comparatives by adding -er
Right: He runs faster than Jacob.
Do not use a comparative adjective unless you have a than in the sentence
Wrong: With winter coming, I will have higher energy bills
Right: I will have higher bills than last year
Pronouns Correct Answer: "This" and "These" are never used as standalone pronouns, nor are "that"
and "those"
Idioms for "ability..." and "capability..." Correct Answer: Wrong: ability of doing...
Right: ability to do...
Right: capability of doing...
Compound Subjects Correct Answer: If two nouns disagree in number with an "or" conjunction, use the
noun closest to the verb to determine agreement
Right: Either the manager or the employees take a break
Right: Either the employees or the manager takes a break
Colon rules Correct Answer: What comes before the colon must be able to stand alone as a sentence
You can insert "namely" or "that is" after the colon, and the result would still be acceptable
Right: I love listening to many kinds of music: namely, classical, rock, rap, and pop
Whatever needs explanation should be placed as close to the colon as possible
Worse: Three factors affect the rate of a reaction: concentration...
Better: The rate of a reaction is affected by three factors: concentration...
The clause after the colon must explain what precedes the colon
What to consume during test Correct Answer: During the break after IR, eat something with protein, fat,
and complex carbs. During the break after Quant, drink glucose (coconut water)
What property do all terminating decimals share? Correct Answer: The simplified denominator of the
decimal must contain only 2's and 5's as prime factors. For example, 7/250 is a terminating decimal
, 0.028, as 250 equals to 2 x 5^3. Fraction 3/30 is also a terminating decimal because 3/30 = 1/10 and
denominator 10 = 2 x 5
"view X as Y" or "view X to be Y" ? Correct Answer: view X as Y
Ex: Many financial experts believe policy makers at the Federal Reserve, now *viewing* the economy
*as* balanced between moderate growth and low inflation, are almost certain to leave interest rates
unchanged.
Is "media" singular or plural? Correct Answer: Plural
Equation for the sum of the degree measures of the n interior angles of a polygon Correct Answer:
180(n - 2)
Each of 90 students participated in at least one of three track tryouts: high jump, long jump, and 100-
meter dash. If 20 students participated in the high jump, 40 students in long-jump, and 60 students in
100-meter dash, and if 5 students participated in all three tryouts, how many students participated in
only two of these tryouts? Correct Answer: Let x be the number who participated in exactly 1 of the
tryouts, y be 2 of tryouts, z be 3 of tryouts. Then x + y + z = 90 and x + 2y + 3z = 120. It is given that z = 5,
so x + y = 85 and x + 2y = 105. Thus, y = *20*
Equation for the sum of the first n terms in an arithmetic sequence Correct Answer: (n/2)(A1 + An)
A train traveled from Station A to B at ave speed of 80 km/hr and from Station B to C at ave speed 60
km/hr. If the train didn't stop at Station B, what was the average speed at which the train traveled from
Station A to C?
1) The distance that the train traveled from A to B was 4 times the distance from B to C
2) The amount of time it took the train to travel from A to B was 3 times the amount of time that it took
the train to travel from B to C Correct Answer: *Time = Dist / Speed*
d1/80 is the amt. of time it took to travel from A to B, and d2/60 is the amt. of time it took to travel from
B to C. We want to find average speed from A to C, given by Total Dist / Total Time = (d1 + d2) / ( (d1/80)
+ (d2/60) )
1) gives d1 = 4d2, which plugged into the above yields an answer
2) gives d1/80 = 3(d2/60), or d1 = 4d2, same as above
Each statement alone is sufficient
A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would
take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car
traveling? Correct Answer: Traveling at 75 km/hr, the car takes 1/75 hr to travel 1 km. In seconds, this
equals 3600/75 = 48 seconds. So this car takes 50 seconds to travel 1 km. In hours, this equals 50/3600 =
1/72 hr. Thus, the speed of the car is 72 km/hr
Is x > 10^10?
