GMAT Math : GMAT Quantitative Reasoning
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Example Questions
Example Question #45 : Dsq: Understanding The Properties Of Integers
A whole number has four digits. True or false: The integer is divisible by 4.
Statement 1: The last digit of the integer is 4.
Statement 2: The sum of the four digits is 20.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Consider the two four-digit whole numbers 5,564 and 5,474. Each ends in 4, and the sum of the digits in each integer is 20, satisfying the conditions of both statements. However, only the first integer is divisible by 4:
The two statements together are therefore insuffcient to answer the question.
Example Question #42 : Arithmetic
True or false: A positive integer 
Statement 1:
Statement 2:
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Assume both statements to be true.
From Statement 1:
Either
From Statement 2:
Either
or
Both equations have the same two solutions, 9 and 11, so it is unclear whether 
A prime number has exactly two factors, 1 and itself. 9 has 3 as a factor, so 9 is not prime; 11 has only 1 and 11 as factors, so 11 is prime. Since either 
Example Question #47 : Dsq: Understanding The Properties Of Integers
Statement 1:
Statement 2: 
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Assume Statement 1 alone. Then:
Either
However, it is given in the problem that 
Assume Statement 2 alone. 3 has only two factors, 1, which is not considered a prime number, and 3, which, having only two factors, is a prime number. Either 
Example Question #48 : Dsq: Understanding The Properties Of Integers
A whole number has four digits. True or false: The integer is divisible by 6.
Statement 1: The last digit in the number is 6.
Statement 2: The sum of the digits in the number is 24.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
A whole number is divisible by 6 if and only if it is divisible by all of the factors of 6, which, other than 1 and 6 itself, are 2 and 3. Therefore, it must be established that the number is divisible by both of these numbers. To be divisible by 2, it is necessary and sufficient that the last digit of the number be 0, 2, 4, 6, or 8. To be divisible by 3, it is necessary and sufficient that the sum of the digits be divisible by 3.
Statement 1 alone, therefore, proves that the number is divisible by 2; however, it does not address divisibility by 3. Similarly, Statement 2 alone proves that the number is divisible by 3 (since 24 is as well), but it does not address divisibility by 2. The two statements together, however, address divisibility by 6, since if both are true, it holds that the number is divisible by both 2 and 3, and, consequently, by 6.
Example Question #42 : Arithmetic
A whole number has four digits. True or false: The integer is divisible by 5.
Statement 1: The last digit is 5.
Statement 2: The sum of the digits is 25.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Assume Statement 1 alone. A necessary and sufficient condition for a whole number to be divisible by 5 is that its last digit be either 0 or 5. By Statement 1, the number meets this requirement, so it is divisible by 5. Statement 2, which gives the digit sum, is therefore, irrelevant.
Example Question #1 : Dsq: Calculating Discrete Probability
Data sufficiency question- do not actually solve the question
A bag of marbles consist of a mixture of black and red marbles. What is the probability of choosing a red marble followed by a black marble?
1. The probability of choosing a black marble first is 
2. There are 10 black marbles in the bag.
Statements 1 and 2 together are not sufficient, and additional information is necessary to answer the question
Each statement alone is sufficient to answer the question
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
From statement 1, we know the probabilty of choosing the first marble. However, since the marble is not replaced, it is impossible to calculate the probability of choosing the second marble. By knowing the information in statement 2 combined with statement 1, we can calculate the total number of marbles initially present.
Example Question #2 : Discrete Probability
A certain major league baseball player gets on base 25% of the time (once every 4 times at bat).
For any game where he comes to bat 5 times, what is the probability that he will get on base either 3 or 4 times? - Hint – add the probability of 3 to the probability of 4.
Binomial Table
Example Question #3141 : Gmat Quantitative Reasoning
A type 1 error (False Alarm or 'Convicting the innocent man') occurs when we incorrectly reject a true null hypothesis.
A type 2 error (failure to detect) occurs when we fail to reject a false null hypothesis.
Which one of the following 5 statements is false?
Note - only 1 of the statements is false.
A) For a given sample size (n=100), decreasing the significane level (from .05 to .01) will decrease the chance of a type 1 error.
B) For a given sample size (n=100), increasing the significane level (from .01 to .05) will decrease the chance of a type 2 error.
C) The ability to correctly detect a false null hypothesis is called the 'Power' of a test.
D) Increasing sample size (from 100 to 120) will always decrease the chance of both a type 1 error and a type 2 error.
E) None of the above statements are true.
B)
A)
C)
D)
E) None of the above statements are true.
E) None of the above statements are true.
Statements A, B, C, and D are all true - so -
The only false statement is E (the statement that declares that A and B and C and D are all false)
Example Question #3141 : Gmat Quantitative Reasoning
A marble is selected at random from a box of red, yellow, and blue marbles. What is the probability that the marble is yellow?
1) There are ten blue marbles in the box.
2) There are eight red marbles in the box.
EITHER Statement 1 or Statement 2 ALONE is sufficient to answer the question.
BOTH statements TOGETHER are NOT sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient.
BOTH statements TOGETHER are NOT sufficient to answer the question.
To determine the probability that the marble is yellow we need to know two things: the number of yellow marbles, and the number of marbles total. The first quantity divided by the last quantity is our probablility.
But the two given statements together only tell us that eighteen marbles are not yellow. This is not enough information. For example, if there are two yellow marbles, the probability of drawing a yellow marble is 
Therefore, the answer is that both statements together are insufficient to answer the question.
Example Question #3 : Discrete Probability
Several decks of playing cards are shuffled together. One card is drawn, shown, and put aside. Another card is dealt. What is the probability that the dealt card is red, assuming the first card is known?
1) The card removed before the deal was red.
2) The cards were shuffled again between the draw and the deal.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.
BOTH statements TOGETHER are insufficient to answer the question.
To answer this question you need to know two things: the number of red cards left and the number of total cards left. The second statement is irrelevant, as a reshuffle does not change the composition of the deck. The first statement tells you that there is one fewer red card than black cards, but it does not tell you how many of each there are, as you do not know how many decks of cards there were.
And that information, which is not given, affects the answer. For example, if there were four decks, there were 103 red cards out of 207; if there were six decks, there were 155 red cards out of 311. The probabilities would be, respectively,
and
a small difference, but nonetheless, a difference.
The correct answer is that both statements together are insufficient to answer the question.
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