Test: Data Interpretation - Super TET MCQ

Values of X and Y that satisfy both the conditions are

More than one value exists for X. Because we are not able to deduce a UNIQUE value for X using the information provided in the two statements together, the given data is NOT sufficient.

Statements TOGETHER are NOT sufficient.

Choice E is the answer.

From statement 1 we know that the square of the means is 36.
From statement 2 we know that the mean of the squares is 56.

Using the formula, Standard deviation = 

we can find the SD of the 4 numbers

Statements TOGETHER are SUFFICIENT.

Choice C is the answer.

We combine the two statements, we know that Bill and Cindy are related to each other through Chris, who is the only brother of Bill and that Cindy is Betty's brother in law's wife.

Cindy does not have any siblings and hence her brother in law has to necessarily be her husband's sibling. As Chris is the only brother of Bill, Cindy's brother in law has to be Bill and Betty is his wife.

Statements TOGETHER are SUFFICIENT.

Choice C is the answer.

Step 1 of solving this GMAT DS question:
Evaluate Statement (1) ALONE: y³ is an integer

We know that y³ is an integer.
However, that does not necessarily mean that y is an integer.
Let us say, y³ = 2, then y is not an integer.
However, if y³ = 8, then y = 2 and is an integer.

Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.

Step 2 of solving this GMAT DS question:
Evaluate Statement (2) ALONE: 3y is an integer

We know that 3y is an integer.
Let us say 3y = 2, then y is not an integer.
However, if 3y = 3, then y will be an integer.

Statement 3 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.

Step 4 of solving this GMAT DS question:
Evaluate Statements (1) & (2) Together: y³ is an integer and 3y is an integer.

Statements TOGETHER are sufficient. Choice C is the answer.

From statement 1, we know the sales value after the salesman's commission is subtracted.

From the question stem, we know his commission is 3% of the sales booked. Then value of sales after subtracting his commission is 100 - 3 = 97% of the sales booked.

Putting the two together, we can deduce that 97% of sales booked = $245,000. So we can find out the sales booked.

Caveat: Do not waste time computing the value. All we need to know is whether the answer will be unique. We know the answer is unique.

Statement 1 ALONE is SUFFICIENT.

Eliminate choices B, C and E.

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From statement 2, we know that the original purchase of the products is $225,000.

We can compute the sales booked as 125% of 225,000 = 1.25 * 225,000.

Caveat: Do not waste time computing the value. All we need to know is whether the answer will be unique. We know the answer is unique.

Statement 2 ALONE is SUFFICIENT.

Each statement is INDEPENDENTLY sufficient. So, choice D is the correct answer to this data sufficiency question.

Evaluate Statement (1) ALONE: x is divisible by 6
Approach: Look for a counter example

Example: x = 6. It is divisible by 6. However, it is NOT divisible by 12.
Counter Example: x = 12. It is divisible by 6. It is divisible by 12 as well.
Knowing that x is divisible by 6 is not enough to answer the question.

If x is divisible by 6, we can infer that it is divisible by 3 and 2. But we cannot deduce whether it is also divisible by 22 - which is essential to deduce that x is divisible by 12.
tatement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.
 

Evaluate Statement (2) ALONE: x is divisible by 8
If x is divisible by 8, then x will definitely be divisible by 4.
However, from statement (2) alone we do not know if x is divisible by 3.
Alternative Approach: Look for a counter example

Example: x = 8. It is divisible by 8. However, it is NOT divisible by 12.
Counter Example:x = 24. It is divisible by 8. It is divisible by 12 as well. 
Knowing that x is divisible by 8 is not enough to answer the question.

Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.
Evaluate Statements (1) & (2) Together: x is divisible by 6 & x is divisible by 8
From statement 1, if x is divisible by 6, it is definitely divisible by 3.
From statement 2, if x is divisible by 8, it is definitely divisible by 4.
So, by combining the two statements, we can conclude that x is divisible by 3 and by 4.
Or that x is divisible by 12.

STATEMENT 1:
Expanding both sides of the inequality, we get a² + b² + 2ab < a² + b² - 2ab
Simplifying we get, 4ab < 0 or ab < 0.
So, we can conclude that ab is not positive. We have got a definite NO as the answer.
Statement 1 ALONE is SUFFICIENT.

Eliminate choices B, C, and E. Answer choices narrow down to A or D.

STATEMENT 2:

This is actually the statement that could trick you.
a = b.
So, either both a and b or positive or both a and b are negative. In either case ab is positive.
We will certainly be "tempted" to decide that statement 2 is also sufficient.
The catch is that, both a and b could be 0. In that case ab = 0, which is not positive.
As we are not able to conclude whether ab is positive with statement 2, it is not sufficient.  Statement 2 ALONE is NOT sufficient.

STATEMENT 1: 

(-1)^{ODD NUMBER} = -1
Therefore, Y + 2 is an odd number.
Hence, Y has to be an odd number.
So, when Y is divided by 2, the remainder is 1.
Statement 1 ALONE is SUFFICIENT.
Eliminate choices B, C, and E. Answer choices narrow down to A or D.

STATEMENT 2:
Y could be '2' which is an even number.
So, if Y is 2, when Y is divided by 2, the remainder is '0'.
All other prime numbers are odd numbers.
So, if Y is one of the other prime numbers, when Y is divided by 2, the remainder is '1'.
We donot have enough data in the question stem or statement 2 to conclude whether Y is 2 or one of the other prime numbers.
As we are not able to conclude whether Y is an even number using statement 2, it is not sufficient.

Statement 2 ALONE is NOT sufficient.
Choice A is the correct answer.

STATEMENT 1: 

(P - 2), P and (P + 2) are 3 consecutive odd integers because (P - 2) and (P + 2) are prime.

One out of 3 consecutive odd integers, (P - 2), P, and (P + 2) will definitely be a multiple of '3'. If (P + 2) and (P - 2) are prime, then P has to be a multiple of '3', which is not prime.

The only exception is if the 3 consecutive odd numbers are 3, 5 and 7. However, we are dealing with two digit positive integers. So that possibility is ruled out.
Statement 1 ALONE is SUFFICIENT.

STATEMENT 2:
This is a brilliant statement.
1. The remainder when (P - 4) and (P - 1) are divided by 3 will be the same.
2. Similarly, the remainder when (P + 4) and (P + 1) are divided by 3 will be the same.
If (P - 4) and (P + 4) are prime, both (P - 4) and (P + 4) will leave a remainder when divided by 3.
Therefore, (P - 1) and (P + 1) will leave a remainder when divided by 3. i.e., they are not divisible by 3.(P - 1), P, (P + 1) are 3 consecutive positive integers.
One out of 3 consecutive integers, (P - 1), P, and (P + 1) will definitely be a multiple of '3'.
If (P - 1) and (P + 1) are not divisible by 3, then P has to be a multiple of '3'. 
P cannot be 3 because when P is 3, (P - 4) will not be prime. So, that possiblity is ruled out.
Therefore, P is not prime.
Statement 2 ALONE is SUFFICIENT.

STATEMENT 1:

If a = b = c = d, the average m will be the same as a.

Since m > a, all the elements in the set cannot be the same, and therefore, s > 0.
Statement 1 ALONE is sufficient.
Eliminate choices B, C and E. Choices narrow down to A and D.

STATEMENT 2:

Approach: Look for a counter example
Example: When a = b = c = d = 0, s = 0
Counter Example: When a = -4, b = 0, c = 0, and d = 4, s > 0
Statement 2 ALONE is NOT sufficient.
Eliminate choice D. Choice A is the answer.

Statement 1: x > 0
We know that x is a positive number.
Interval 1: If 0 < x < 1, then x3 < x².
For example, (0.5)3 = 0.125, which is lesser than (0.5)2 = 0.25
The answer to the question is NO.
Interval 2: If x > 1, then x³ > x²
For example, 23 = 8 which is greater than 22 = 4
The answer to the question is YES.
We do NOT have a DEFINITE answer using statement 1.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.

Evaluate Statement (2) ALONE
Statement 2: x < 1
Interval 1: For positive values of x, i.e., 0 < x < 1, we know x³ < x².
The answer to the question is NO.

Interval 2:For negative values of x, x³ will be a negative number and x² will be a positive number.
Hence, x³ < x² 
The answer to the question is NO.

Lastly, what is the answer if x = 0?
When x = 0, x³ = x².
The answer to the question is NO.

Hence, if we know that x < 1, we can conclude that x³ is NOT GREATER THAN x².
We have a DEFINITE answer, even if it is NO.

Statement 2 ALONE is sufficient. Eliminate choices C and E.

Choice B is the answer.

Evaluate Statement (1) ALONE: (y - 3)(x - 4) = 0
If product of the two terms (y - 3) and (x - 4) is 0, then at least one of the two terms equals 0.
(y - 3) = 0 or (x - 4) = 0 or both (y - 3) and (x - 4) equal 0.
i.e., either y = 3 or x = 4 or that both y = 3 and x = 4.
If x = 4, y could take any value. The value of 'y' could be 3 or it could be some other value and the product will still be a 0.
Example: x = 4 and y = 5. The equation holds good. y ≠ 3.
Counter example: x = 4 and y = 3. The equation holds good. y = 3
We CANNOT determine whether 'y' is 3 from this statement.

Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E

Evaluate Statement (2) ALONE: (x - 4) = 0
The statement provides no information about y.

Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.

 

Evaluate Statements (1) & (2) Together: (y - 3)(x - 4) = 0 & (x - 4) = 0
When x = 4, (y - 3)(x - 4) will be 0 irrespective of the value that y takes.

Can 'y' be 3? Yes 'y' can be 3.
Is y = 3? Not necessary.It can take values other than 3 and the data in the two statements will still hold good.

Eliminate choice C.
Statements TOGETHER are NOT sufficient. Choice E is the answer.

Evaluate Statement (1) ALONE 
Statement (1) : x is a multiple of 2

No information about y has been provided.
Approach: Let us look for a counter example.

Example: When x = 2 and y = 3, x/y is non-terminating.
The answer to the question is NO.

Counter Example: When x = 2 and y = 4, x/y is terminating.
The answer to the question is YES.

We have found a counter example. Therefore, statement 1 does not provide a DEFINITE answer.

Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.
 

Evaluate Statement (2) ALONE 
Statement (2) : y is a multiple of 3

No information about x has been provided.
Approach: Let us look for a counter example.

Example:When x = 3 and y = 3, xyxy is terminating.
The answer to the question is YES.

Counter Example: When x = 2 and y = 3, xyxy is non-terminating.
The answer to the question is NO.

We have found a counter example. Therefore, statement 2 does not provide a DEFINITE answer.

Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.
Evaluate Statements (1) & (2) Together 
Statements Together : x is a multiple of 2 & y is a multiple of 3
Approach: Let us look for a counter example.

Example:When x = 6 and y = 6, x/y is terminating.
The answer to the question is YES.

Counter Example: When x = 2 and y = 3, x/y is non-terminating.
The answer to the question is NO.

We have found a counter example. Despite combining the information in the statements we are not able to find a DEFINITE answer.

Statements TOGETHER are NOT SUFFICIENT. Choice E is the answer.

Evaluating Statement (1) ALONE
Statement (1) : When X is divided by 14, the remainder is 4
The number is, therefore, of the form 14k + 4.
It will leave a remainder of 4 when divided by 7. (14k is divisible by 7. When 4 is divided by 7, the remainder is 4.)

This number is definitely not divisible by 7.
To be divisible by 21, the number must be divisible by both 3 and 7. This number is not divisible by 7. Hence, X is not divisible by 21.

We have a DEFINITE NO as the answer to the question using statement 1.

Statement 1 ALONE is sufficient.
Eliminate choices B, C and E. Choices narrow down to A or D.
 

Evaluating Statement (2) ALONE
Statement (2) : When X is divided by 15, the remainder is 5
The number X is of the form 15m + 5
Therefore, the number will leave a remainder of 2 when divided by 3.

Hence, it is not divisible by 3.
To be divisible by 21, the number must be divisible by both 3 and 7. This number is not divisible by 3. Hence, X is not divisible by 21.

We have a DEFINITE NO as the answer to the question using statement 2 as well.

Statement 2 ALONE is also sufficient.
Eliminate choice A.

Each statement is INDEPENDENTLY sufficient. Choice D is the answer.

The correct answer is E. i.e., Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Explanatory Answer
Statement 1: It is obvious that statement 1 is not sufficient. Data given does not provide any information about the value of b. So, we can eliminate choices A and D. So we are down to choices B, C or E.

Statement 2: An equation with two variables ‘a’ and ‘b’. Hence, the information provided is not sufficient.

Note do not make the mistake of solving the equation as either (a – 3) = 0 or (b + 2) = 0 and decide that b = -2. What if only (a – 3) = 0 and (b + 2) was not ‘0’.

Combining the two statements, we know a = 3, so, (a – 3) = 0. But that leaves the question of what (b + 2) or what ‘b’ is unanswered.

Hence, choice D is the correct answer.