xy = 10^n

Question

x and y are positive integers such that xy = 10^n. If x>y, the units digit of x-y CANNOT be A) 1 B) 3 C) 5 D) 7 E) 9

parallel_chase · Answer

Brent Hanneson wrote:x and y are positive integers such that xy = 10^n. If x>y, the units digit of x-y CANNOT be
A) 1
B) 3
C) 5
D) 7
E) 9

xy=10^n

x>y

x =5 , y= 2 , x-y = 3

x = 25, y = 4, x-y = 1

x = 10, y = 1, x-y = 9

x = 25, y = 8, x-y = 7

Hence 5.

aroon7 · Answer

parallel_chase wrote:Brent Hanneson wrote:x and y are positive integers such that xy = 10^n. If x>y, the units digit of x-y CANNOT be A) 1 B) 3 C) 5 D) 7 E) 9 xy=10^n x>y x =5 , y= 2 , x-y = 3 x = 25, y = 4, x-y = 1 x = 10, y = 1, x-y = 9 x = 25, y = 8, x-y = 7 Hence 5. x=200, y=5, x-y = 195. so not 5 Ans is 7 when x= 25, y=8, we get xy = 200. this is not nth power of 10... what is the OA? thanks!

parallel_chase · Answer

aroon7 wrote:parallel_chase wrote:Brent Hanneson wrote:x and y are positive integers such that xy = 10^n. If x>y, the units digit of x-y CANNOT be A) 1 B) 3 C) 5 D) 7 E) 9 xy=10^n x>y x =5 , y= 2 , x-y = 3 x = 25, y = 4, x-y = 1 x = 10, y = 1, x-y = 9 x = 25, y = 8, x-y = 7 Hence 5. x=200, y=5, x-y = 195. so not 5 Ans is 7 when x= 25, y=8, we get xy = 200. this is not nth power of 10... what is the OA? thanks! There was a typo x = 125, y = 8, x-y = 7 xy = 1000 = 10^n x = 200, y = 5, x-y = 5 I guess the correct option is missing or I am missing something ?

Brent@GMATPrepNow · Answer

Man, what a bad day for me.
I think this might be my last post, since I have now posted 2 questions with missing/incorrect information.

The question needs the proviso, "x and y" are not multiples of 10.
If we add that proviso, the correct answer is C (5).

Yikes - pretty sloppy stuff.
Sorry to all those who spent a great deal of time on this poorly-constructed question.

Brent Hanneson - Creator of GMATPrepNow.com

parallel_chase · Answer

Brent Hanneson wrote:Man, what a bad day for me.
I think this might be my last post, since I have now posted 2 questions with missing/incorrect information.

The question needs the proviso, "x and y" are not multiples of 10.
If we add that proviso, the correct answer is C (5).

Yikes - pretty sloppy stuff.
Sorry to all those who spent a great deal of time on this poorly-constructed question.

I hope these 2 questions dont stop you from drafting questions in future

2 bad out of 20 awesome questions- I am sure we can live with that

Its a pleasure having you on this forum.

Thanks.

Brent@GMATPrepNow · Answer

Thanks PC. I'll continue to create questions, but perhaps I better quadruple check them in the future.

Ian Stewart · Answer

Brent Hanneson wrote:Man, what a bad day for me.
I think this might be my last post

I hope not- it's clear that many people here have appreciated your questions, and I think everyone here understands that designing questions can be a tricky thing to do, especially when a question doesn't follow a pre-existing model. One of the more interesting facts that I found reading the legal documents from the GMAC/ScoreTop lawsuit: to design one official GMAT question, GMAC spends, on average, $2400, which should give people some idea of how much work goes into this (and why it's so hard to emulate the real thing).

Brent Hanneson wrote: The question needs the proviso, "x and y" are not multiples of 10.
If we add that proviso, the correct answer is C (5).

As a suggestion, it might be more elegant to say that the GCD of x and y is 1, rather than to say that neither is a multiple of 10. It's a nice question, just as long as some kind of condition is added.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Brent@GMATPrepNow · Answer

I love your suggestion to note that the gcd=1. Much more eloquent than saying that neither value is a multiple of 10.

It reminds me of the popular GMAT proviso "xy is not equal zero," rather than saying "x is not equal to zero and y is not equal to zero"

Brent Hanneson - Creator of GMATPrepNow.com

Brent@GMATPrepNow · Answer

I just realized that I wrote "this might be my last post" when I meant to say "this might be my last post for the day"
"last post ever" is overly dramatic given the situation.
Yet another error

Looks like someone didn't get enough sleep last night.

Brent Hanneson - Creator of GMATPrepNow.com

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