Test: Arithmetic - GMAT MCQ

Statement (1) alone: The length of the longest piece is twice the length of the shortest piece.

From this statement alone, we cannot determine the specific lengths of the pieces. We only know that the longest piece is twice the length of the shortest piece, but we don't have any information about the middle piece. Therefore, statement (1) alone is not sufficient.

Statement (2) alone: The sum of the length of the two shorter pieces is 15 meters.

From this statement alone, we know that the sum of the lengths of the two shorter pieces is 15 meters. However, we don't know how these lengths are distributed between the pieces. It is possible that one of the shorter pieces is much longer than the other, making the longest piece longer than the other two combined. Alternatively, the lengths of the two shorter pieces could be equal, resulting in a longer longest piece. Without further information, we cannot determine the length of the longest piece based on statement (2) alone. Therefore, statement (2) alone is not sufficient.

Since neither statement alone is sufficient to answer the question, the correct answer is option B: Statement (2) alone is sufficient, but statement (1) alone is not sufficient to answer the question asked.

To determine if the ratio j/k is a terminating decimal, we need to consider both statements.

Statement (1) tells us that k = 3. If k is equal to 3, it means the denominator has a prime factor of 3. Since any power of 3 in the denominator will result in a repeating decimal, we can conclude that the ratio j/k is not a terminating decimal. Therefore, statement (1) alone is sufficient to answer the question.

Statement (2) tells us that j is an odd multiple of 3. This information alone does not provide any details about the denominator k or the factors of k. It does not give us enough information to determine if the ratio j/k is a terminating decimal. Therefore, statement (2) alone is not sufficient to answer the question.

When we consider both statements together, we know that k = 3 (from statement 1) and j is an odd multiple of 3 (from statement 2). Since the denominator is 3, which has a prime factor of 3, the ratio j/k will not be a terminating decimal. Therefore, both statements together are sufficient to answer the question.

Hence, the answer is C: BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient.

Statement (1) tells us that the ratio of the number of packets bought by Maria containing 30 tablets to the number of packets containing 90 tablets is 3:2. However, this statement alone does not provide any information about the number of packets containing 60 tablets or the total number of packets bought by Maria. We cannot determine the total number of packets bought based on this statement alone.

Statement (2) tells us that the number of packets bought by Maria containing 60 tablets is half of the total number of packets bought by Maria. However, this statement does not provide any information about the number of packets containing 30 or 90 tablets. We cannot determine the total number of packets bought based on this statement alone.

When we consider both statements together, we still cannot determine the exact number of packets bought by Maria. Statement (1) gives us the ratio of packets containing 30 tablets to packets containing 90 tablets, but we don't know the actual number of packets. Statement (2) provides information about the packets containing 60 tablets but does not give us any information about the other packet sizes. Without knowing the specific quantities for each packet size, we cannot calculate the total number of packets bought.

Therefore, the correct answer is E: Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

To find the difference between a pair of temperatures on the Celsius scale, we need to determine the difference between their corresponding temperatures on the Fahrenheit scale.

Statement (1) tells us that the difference between the temperatures on the Fahrenheit scale is 45°. This information alone is sufficient to calculate the difference in Celsius. We can use the formula C = (5/9)(F - 32) to convert the Fahrenheit difference to Celsius. Therefore, statement (1) alone is sufficient to answer the question.

Statement (2) tells us that the greater of the two temperatures is 30° on the Celsius scale. However, this statement does not provide any information about the difference between the temperatures or the corresponding Fahrenheit values. It does not give us enough information to calculate the difference between the temperatures on the Celsius scale. Therefore, statement (2) alone is not sufficient to answer the question.

When we consider both statements together, statement (1) provides us with the difference between the Fahrenheit temperatures, and statement (2) gives us information about the greater temperature on the Celsius scale. However, we still cannot determine the exact difference between the temperatures on the Celsius scale. We need the corresponding Fahrenheit values to calculate that. Therefore, both statements together are not sufficient to answer the question.

Hence, the answer is A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Statement (1) states that if there were 10 more students in his class, Professor Garcia would have at least 50 students. This means that the current number of students is less than 50, but we don't have an exact value. Therefore, statement (1) alone is not sufficient to answer the question.

Statement (2) states that if there were 10 fewer students in his class, Professor Garcia would have at most 50 students. This means that the current number of students is more than 40, but again, we don't have an exact value. Therefore, statement (2) alone is not sufficient to answer the question.

When we consider both statements together, we know that the number of students is between 40 and 50 (exclusive range). However, we still don't have an exact value or a narrow range within this interval. Without additional information, we cannot determine the precise number of students Professor Garcia currently has in his class.

Thus, the answer is E: Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Statement (1) tells us that when d is rounded to the nearest tenth, the result is 1.6. Since 1.6 is greater than 1.55, we can conclude that d is greater than or equal to 1.55. Therefore, statement (1) alone is sufficient to answer the question.

Statement (2) tells us that when d is rounded to the nearest integer, the result is 2. However, this information does not provide a direct comparison to 1.55. We cannot determine if d is greater than or equal to 1.55 based on this statement alone. Therefore, statement (2) alone is not sufficient to answer the question.

When we consider both statements together, statement (1) provides a direct comparison indicating that d is greater than or equal to 1.6. However, statement (2) does not provide any additional information related to the comparison of d to 1.55. Therefore, both statements together do not provide enough information to answer the question.

Hence, the answer is A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

To find the arithmetic mean of 3x and 4y, we need to calculate (3x + 4y)/2.

Let's analyze each statement:

Statement (1) tells us that y/6 - x/8 = 2/3. This equation alone does not directly provide information about the arithmetic mean of 3x and 4y. It relates x and y in terms of fractions, but it does not give us specific values for x or y. Therefore, statement (1) alone is not sufficient to answer the question.

Statement (2) tells us that y/6 + x/8 = 5/3. This equation alone also does not directly provide information about the arithmetic mean of 3x and 4y. It relates x and y in terms of fractions, but it does not give us specific values for x or y. Therefore, statement (2) alone is not sufficient to answer the question.

When we consider both statements together, we have the following system of equations:

y/6 - x/8 = 2/3 (from statement 1) y/6 + x/8 = 5/3 (from statement 2)

By adding these two equations, we eliminate the x term:

(2y/6) + (2x/8) = 7/3

Simplifying:

y/3 + x/4 = 7/3

From this equation, we still cannot determine the values of x and y separately, and therefore, we cannot find the arithmetic mean of 3x and 4y.

Hence, the answer is B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

To determine the number of multiples of 4 in 5 consecutive integers, let's analyze each statement:

Statement (1) tells us that the median of the five consecutive integers is 4. Since there are five integers, the middle number must be 4. Let's assume the five consecutive integers are x, x+1, x+2, x+3, and x+4. Since 4 is the median, we have (x+2) = 4, which implies x = 2. Therefore, the five consecutive integers are 2, 3, 4, 5, and 6. Among these, there is only one multiple of 4, which is 4 itself. Hence, statement (1) alone is sufficient to answer the question.

Statement (2) tells us that the average (arithmetic mean) of the five consecutive integers is a multiple of 4. Let's assume the five consecutive integers are a, b, c, d, and e. We can express the average as (a+b+c+d+e)/5. If this average is a multiple of 4, it means that the sum a+b+c+d+e must be divisible by 4. However, statement (2) does not provide any specific values for a, b, c, d, and e, or their relationships, so we cannot determine the number of multiples of 4. Hence, statement (2) alone is not sufficient to answer the question.

When we consider both statements together, we know that the median is 4 (statement 1) and the average is a multiple of 4 (statement 2). From statement 1, we can determine that the five consecutive integers are 2, 3, 4, 5, and 6. From statement 2, we know that the sum of these integers is a multiple of 4. The sum is 2+3+4+5+6 = 20, which is divisible by 4. Therefore, the number of multiples of 4 in these five consecutive integers is 1.

Thus, each statement alone is sufficient to answer the question. The answer is D: EACH statement ALONE is sufficient to answer the question asked.

Statement (1) alone: The total given work is greater than 80 units.

If the total given work is greater than 80 units, this information alone does not provide any insight into whether 4 boys and 3 girls can finish the work within 6 days. We still need to know the combined work capacity of the boys and girls.

Statement (2) alone: The total given work is lesser than 100 units.

If the total given work is lesser than 100 units, this information alone does not give us enough information to determine if 4 boys and 3 girls can complete the work within 6 days. We need to know the combined work capacity of the boys and girls.

Combining the statements:
When we combine the statements, we still don't have specific information about the work capacity of 4 boys and 3 girls in 6 days. Therefore, the combined statements are not sufficient to answer the question.

Since statement (2) alone is sufficient to answer the question while statement (1) alone is not, the correct answer is (B): Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.