For any integers x and y, min(x,y) and max(x,y) denote the minimum and

Question

For any integers x and y, min(x,y) and max(x,y) denote the minimum and the maximum of x and y, respectively. For example, min(5,2)=2 and max(5,2)=5. For the integers a and b, what is the value of max(a,b)?

(1) a > b

(2) ab = −1

(1) a > b

(2) ab = −1

Bunuel · Accepted Answer

For any integers x and y, min(x,y) and max(x,y) denote the minimum and the maximum of x and y, respectively. For example, min(5,2)=2 and max(5,2)=5. For the integers a and b, what is the value of max(a,b)?

(1) a > b --> max(a, b) = a but since we don't know the numerical value of a, then this statement is not sufficient.

(2) ab = −1. Since a and b are integers, then a = 1 and b = -1 or vise-versa. In any case, max(a, b) = 1. Sufficient.

Answer: B.

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Hope it helps.

chandra004 · Answer

Hello  Bunuel 
I've one question here:-
for 2) even this is the possibility, a = -1/2 and b = 2 or a = -2 and b = 1/2. Here also we don't have definite value for a or b. Then this statement must not be sufficient?

Bunuel · Answer

Notice that the function is given to be defined for integers only.

MHIKER · Answer

We need to figure out a definite value, not a variable.

(1) It gives "a" not any numerical value; Insufficient.

(2)  ab=-1 , that is  -1*1 , either  a=-1  or  b=-1  it will not matter as the will take the maximum value that will be definite 1. Sufficeint.

The answer is B

HarshavardhanR · Answer

(1) a > b

While this tells us that max(a,b) = a, we have no idea what the actual value of "a" is. Hence statement 1 is not sufficient to find the value of max(a,b).

(2) ab = -1

Given the condition that ->  a and b are integers

The above is only possible if either

-> a = 1; b = -1 OR
-> a = -1; b = 1

In either case, max (a, b) = the max value between -1 and +1 = +1.

So, statement 2 is sufficient to find the value of max(a,b).

Answer: Choice B

---
Harsha

Riyaagoell · Answer

In my opinion, the question can be answered by either of the statements as the question doesn't specify that the answer has to be numerical. As 'a' is an integer in the first statement the answer will also be an integer.

Bunuel · Answer

No, you are wrong here. This is a value question. When a Data Sufficiency question asks for a value, a statement is sufficient only if it determines one specific numerical value. Statement (1) tells us only that max(a, b) = a, but it does not determine the numerical value of a.

MarkGMATMentor · Answer

This problem contains a common DS trap: a statement doesn't allow you to solve for individual variables but is still sufficient.

Here, the prompt defines two functions (min and max) that each have two inputs. So, it's easy to assume that you need to know the values of both a and b to answer the question.

Statement 1:
 By itself, this statement gives you no actual values, only relative size, so it is clearly  insufficient.

Statement 2:
 Since a and b must both be integers, there are only two possibilities: either a = 1 and b = -1, or a = -1 and b = 1. Only if you include the first statement will you know which possibility is correct, which could lead you to pick choice C.

However, the question isn't asking for the values of a and b individually, but the value of max(a,b). Whether a = 1 or b = 1, the maximum value is 1. This statement is  sufficient  alone and the answer is B.

Always make sure you understand what the question is asking for up front, and when you answer, confirm that you're answering the right question.

This will help you avoid traps like this one. Another common example is when a question asks for the value of x + y and there is no way to solve for x or y individually, yet you are still able to determine the sum.

For any integers x and y, min(x,y) and max(x,y) denote the minimum and

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GMAT Data Sufficiency (DS) Questions

For any integers x and y, min(x,y) and max(x,y) denote the minimum and

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

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Perfect 805 Score Debrief by Julia

My Rewards