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.

Similar questions to practice:
https://gmatclub.com/forum/max-x-y-is-d ... 28330.html
https://gmatclub.com/forum/for-any-inte ... 94998.html
https://gmatclub.com/forum/for-any-inte ... 61903.html

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

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

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

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

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards