Data Sufficiency Online Test: Quiz!

1. If the Longfellow Playground is rectangular, what is its width? (1) The ratio of its length to its width is 7 to 2. (2) The perimeter of the playground is 396 meters.

A. if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

B if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient;

C. if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

D. if EACH statement ALONE is sufficient to answer the question;

E. if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question.

Statement (1) provides the ratio of the length to the width, but it does not give any specific values for either the length or the width. Therefore, statement (1) alone is not sufficient to determine the width of the Longfellow Playground.

Statement (2) provides the perimeter of the playground, but it does not give any information about the dimensions or shape of the playground. Therefore, statement (2) alone is not sufficient to determine the width of the Longfellow Playground.

However, if we combine both statements, we can use the ratio from statement (1) to set up a system of equations and solve for both the length and the width. Therefore, the two statements taken together are sufficient to answer the question.

Explanation

Statement (1) provides the ratio of the length to the width, but it does not give any specific values for either the length or the width. Therefore, statement (1) alone is not sufficient to determine the width of the Longfellow Playground.

Statement (2) provides the perimeter of the playground, but it does not give any information about the dimensions or shape of the playground. Therefore, statement (2) alone is not sufficient to determine the width of the Longfellow Playground.

However, if we combine both statements, we can use the ratio from statement (1) to set up a system of equations and solve for both the length and the width. Therefore, the two statements taken together are sufficient to answer the question.

2. What is the value of x –1? (1) x + 1 =3 (2) x – 1 < 3

A. if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

B if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient;

C. if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

D. if EACH statement ALONE is sufficient to answer the question;

E. if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question.

Statement (1) tells us that x + 1 = 3. By subtracting 1 from both sides of the equation, we can determine that x = 2. Therefore, statement (1) alone is sufficient to answer the question. However, statement (2) does not provide any information about the value of x, so it is not sufficient on its own. Therefore, the correct answer is A.

Explanation

Statement (1) tells us that x + 1 = 3. By subtracting 1 from both sides of the equation, we can determine that x = 2. Therefore, statement (1) alone is sufficient to answer the question. However, statement (2) does not provide any information about the value of x, so it is not sufficient on its own. Therefore, the correct answer is A.

3. Is ΔMNP isosceles? (1) Exactly two of the angles, ∠M and ∠N, have the same measure (2) ∠N and ∠P do not have the same measure.

A. if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

B if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient;

C. if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

D. if EACH statement ALONE is sufficient to answer the question;

E. if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question.

Statement (1) states that exactly two angles, ∠M and ∠N, have the same measure. This implies that the triangle has two equal angles, making it an isosceles triangle. However, statement (2) does not provide any information about the angles of the triangle, so it is not sufficient to determine if the triangle is isosceles or not. Therefore, statement (1) alone is sufficient to answer the question, but statement (2) alone is not sufficient.

Explanation

Statement (1) states that exactly two angles, ∠M and ∠N, have the same measure. This implies that the triangle has two equal angles, making it an isosceles triangle. However, statement (2) does not provide any information about the angles of the triangle, so it is not sufficient to determine if the triangle is isosceles or not. Therefore, statement (1) alone is sufficient to answer the question, but statement (2) alone is not sufficient.

4. Is William taller than Jane? (1) William is taller than Anna. (2) Anna is not as tall as Jane.

A. if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

B if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient;

C. if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

D. if EACH statement ALONE is sufficient to answer the question;

E. if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question.

Statement (1) tells us that William is taller than Anna, but it does not provide any information about Jane's height. Statement (2) tells us that Anna is not as tall as Jane, but it does not provide any information about William's height. Therefore, even when both statements are considered together, we still cannot determine whether William is taller than Jane. Hence, the two statements taken together are still not sufficient to answer the question.

Explanation

Statement (1) tells us that William is taller than Anna, but it does not provide any information about Jane's height. Statement (2) tells us that Anna is not as tall as Jane, but it does not provide any information about William's height. Therefore, even when both statements are considered together, we still cannot determine whether William is taller than Jane. Hence, the two statements taken together are still not sufficient to answer the question.

5. In parallelogram ABCD , what is the measure of ∠ADC? (1) The measure of ∠ABC is greater than 90^o. (2) The measure of ∠BCD is 70^o

A. if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

B if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient;

C. if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

D. if EACH statement ALONE is sufficient to answer the question;

E. if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question.

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Explanation

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6. In ΔPQR, what is the value of x ?

(1) PQ = PR (2) y = 40

A. if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

B if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient;

C. if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

D. if EACH statement ALONE is sufficient to answer the question;

E. if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question.

According to statement (1) PQ = PR; therefore, ΔPQR is isosceles and y = z. Since x + y + z =
180, it follows that x + 2y = 180. Since statement (1) does not give a value for y, you cannot answer the
question using statement (1) alone. According to statement (2), y = 40; therefore, x + z = 140. Since
statement (2) does not give a value for z, you cannot answer the question using statement (2) alone.
Using both statements together, since x + 2y = 180 and the value of y is given, you can ﬁ nd the value
of x. Therefore, BOTH statements (1) and (2) TOGETHER are sufﬁ cient to answer the questions, but
NEITHER statement ALONE is sufﬁ cient.

Explanation

According to statement (1) PQ = PR; therefore, ΔPQR is isosceles and y = z. Since x + y + z =
180, it follows that x + 2y = 180. Since statement (1) does not give a value for y, you cannot answer the
question using statement (1) alone. According to statement (2), y = 40; therefore, x + z = 140. Since
statement (2) does not give a value for z, you cannot answer the question using statement (2) alone.
Using both statements together, since x + 2y = 180 and the value of y is given, you can ﬁ nd the value
of x. Therefore, BOTH statements (1) and (2) TOGETHER are sufﬁ cient to answer the questions, but
NEITHER statement ALONE is sufﬁ cient.

7. Is x² equal to xy? (1) x² – y² = (x + 5)(y - 5) (2) x = y

A. if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

B if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient;

C. if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

D. if EACH statement ALONE is sufficient to answer the question;

E. if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question.

Statement (1) provides an equation expressing the difference of squares, but it does not provide any information about the relationship between x^2 and xy. Therefore, it is not sufficient to answer the question. However, statement (2) states that x is equal to y. If x = y, then x^2 will be equal to xy. Therefore, statement (2) alone is sufficient to answer the question.

Explanation

Statement (1) provides an equation expressing the difference of squares, but it does not provide any information about the relationship between x^2 and xy. Therefore, it is not sufficient to answer the question. However, statement (2) states that x is equal to y. If x = y, then x^2 will be equal to xy. Therefore, statement (2) alone is sufficient to answer the question.

8. For which type of investment, J or K, is the annual rate of return greater? (1) Type J returns $115 per $1,000 invested for any one-year period, and type K returns $300 per $2,500 invested for any one-year period. (2) The annual rate of return for an investment of type K is 12 percent.

A. if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

B if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient;

C. if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

D. if EACH statement ALONE is sufficient to answer the question;

E. if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question.

Statement (1) provides the returns for both types of investments, but it does not provide the rate of return. Therefore, we cannot determine which type of investment has a greater annual rate of return based on this statement alone.

Statement (2) provides the annual rate of return for type K, which is 12 percent. This allows us to compare the rate of return for type K with the returns provided in statement (1) and determine that the annual rate of return for type K is greater.

Therefore, statement (2) alone is sufficient to answer the question, but statement (1) alone is not sufficient. The correct answer is B.

Explanation

Statement (1) provides the returns for both types of investments, but it does not provide the rate of return. Therefore, we cannot determine which type of investment has a greater annual rate of return based on this statement alone.

Statement (2) provides the annual rate of return for type K, which is 12 percent. This allows us to compare the rate of return for type K with the returns provided in statement (1) and determine that the annual rate of return for type K is greater.

Therefore, statement (2) alone is sufficient to answer the question, but statement (1) alone is not sufficient. The correct answer is B.

9. What was John's average driving speed in miles per hour during a 15-minute interval? (1) He drove 10 miles during this interval. (2) His maximum speed was 50 miles per hour and his minimum speed was 35 miles per hour during this interval.

A. if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

B if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient;

C. if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

D. if EACH statement ALONE is sufficient to answer the question;

E. if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question.

Statement (1) alone tells us that John drove 10 miles during the 15-minute interval. However, it does not provide any information about the time it took him to drive those 10 miles. Without knowing the time, we cannot calculate the average driving speed.

Statement (2) alone tells us the maximum and minimum speeds during the interval, but it does not provide any information about the distance traveled or the time taken. Without knowing either of these, we cannot calculate the average driving speed.

However, if we combine the information from both statements, we know that John drove 10 miles during the 15-minute interval and his maximum speed was 50 miles per hour, while his minimum speed was 35 miles per hour. With this information, we can calculate the average driving speed by dividing the total distance (10 miles) by the total time (15 minutes). Therefore, the two statements taken together are sufficient to answer the question.

Explanation

Statement (1) alone tells us that John drove 10 miles during the 15-minute interval. However, it does not provide any information about the time it took him to drive those 10 miles. Without knowing the time, we cannot calculate the average driving speed.

Statement (2) alone tells us the maximum and minimum speeds during the interval, but it does not provide any information about the distance traveled or the time taken. Without knowing either of these, we cannot calculate the average driving speed.

However, if we combine the information from both statements, we know that John drove 10 miles during the 15-minute interval and his maximum speed was 50 miles per hour, while his minimum speed was 35 miles per hour. With this information, we can calculate the average driving speed by dividing the total distance (10 miles) by the total time (15 minutes). Therefore, the two statements taken together are sufficient to answer the question.

10. Was 70 the average (arithmetic mean) grade on a class test? (1) On the test, half of the class had grades below 70 and half of the class had grades above 70. (2) The lowest grade on the test was 45 and the highest grade on the test was 95.

A. if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient;

B if statement (2) ALONE is sufficient to answer the question but statement (1) alone is not sufficient;

C. if the two statements TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient;

D. if EACH statement ALONE is sufficient to answer the question;

E. if the two statements TAKEN TOGETHER are still NOT sufficient to answer the question.

Statement (1) alone is sufficient to answer the question. If half of the class had grades below 70 and half had grades above 70, then the average grade would be exactly 70. However, statement (2) does not provide any information about the distribution of grades, so it is not sufficient on its own. Therefore, the correct answer is A.

Explanation

Statement (1) alone is sufficient to answer the question. If half of the class had grades below 70 and half had grades above 70, then the average grade would be exactly 70. However, statement (2) does not provide any information about the distribution of grades, so it is not sufficient on its own. Therefore, the correct answer is A.