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Example Questions
Example Question #42 : 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.
EITHER 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.
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 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 is prime.
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
, in which case
, or
, in which case
.
From Statement 2:
Either
or
Both equations have the same two solutions, 9 and 11, so it is unclear whether or
.
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 or
, it is not clear whether
is prime or not.
Example Question #47 : Dsq: Understanding The Properties Of Integers
is a positive integer. True or false:
is prime.
Statement 1:
Statement 2: is a factor of 3.
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
, in which case
, or
, in which case
.
However, it is given in the problem that is a positive integer, so
, which is not considered to be a prime number, since it does not have exactly two factors.
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 or
, so without further information, it is not clear whether
is prime.
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 #3141 : Gmat Quantitative Reasoning
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.
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.
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.
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
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
Statements 1 and 2 together are not sufficient, and additional information is necessary to answer the question
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 : Dsq: Calculating 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 #1031 : Data Sufficiency Questions
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)
D)
C)
E) None of the above statements are true.
A)
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 #3 : Dsq: Calculating Discrete Probability
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 . But if there are twenty-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 #4 : Dsq: Calculating Discrete Probability
Data sufficiency question
What is the probability of choosing a red marble at random from a bag filled with marbles?
1. There are only red and black marbles in the bag
2. of the marbles are black
each statement alone is sufficient
both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
From statement 1, we learn that there are only two different colored marbles in the bag. From statement 2, we learn that are black which tells us that
are red. Without statement 1, it is impossible to determine if there is another color of marble in the bag.
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