Is K an integer? (1) K=P/Q, where P and Q are consequtive

Question

Guys! Where are you all?

Is K an integer?

(1) K=P/Q, where P and Q are consequtive integers;
(2) K=N^N, where N is an integer

stolyar · Answer

Some are still alive... Yes, it is E. :band

tzolkin · Answer

Ans : E

1) if P and Q +ve, ans N
if P and Q -ve, ans Y

2) if N +ve, ans Y
if N -ve ans N

Combined. There is NO solution for P/Q=N^N
(so K cannot be an integer but there is also no solution)

stolyar · Answer

The trick with (1) is not positive vs. negative, but 0/1 vs. 7/8
Also Q cannot be a zero -- a sufficient condition to say no.

(2) what if N=0?

tzolkin · Answer

for 

1) say p=-2 and q=-1 then P/Q = 2 (this is why I mentioned + -ve)

2) 2^2 = 4
-2^(-2) = -1/4

Combined
0^0 = 1 and no P/Q will be 1

Any thoughts ?

Why can't q=0 ? -1,0,1,2 etc....

stolyar · Answer

Be careful with 0^0. It is not always equal to a zero?

tzolkin · Answer

The discussion of 0^0 is very old. Euler argues for 0^0 = 1 since a^0 = 1 for a not equal to 0 . The controversy raged throughout the nineteenth century, but was mainly conducted in the pages of the lesser journals: Grunert's Archiv and Schlomilch's Zeitshrift. Consensus has recently been built around setting the value of 0^0 = 1.

If 0^0 = 0 then 0/1=0 then N^N = P/Q and ans would be C

stolyar · Answer

It is the first time I have heard that it is legal to say that 0^0=1. From my university course of math I remember that the case is uncertain. It can be 1, but not always, depending on a function.

rite2deepti · Answer

My answer is A as P and Q are consecutive integers and 0 is not an integer that means we can have P=1,Q=2 P/Q not an integer .Sufficient

For statement 2 N^N where N is an integer we can have N -ve as well as +ve so not sufficient

Bunuel · Answer

First of all: zero is an integer. Moreover it's an even integer.

Next, the case of 0^0 is not tested on GMAT.

This is poorly written question (definitely not GMAT type), so I wouldn't worry about it.

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.

Is K an integer? (1) K=P/Q, where P and Q are consequtive

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

Is K an integer? (1) K=P/Q, where P and Q are consequtive

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