f(x) is the remainder of n divided by x. If x is a positive

Question

f(x) is the remainder of n divided by x. If x is a positive integer, is x greater than 20?

1) f(x+10)=42
2) f(bx)=36

scthakur · Answer

A for me.
stmt1: f(x+10) is the remainder of (x+10)/n and is equal to 42. Thus, n > 42 and (x+10) should at least be equal to 42. That means, x = 32. Hence, sufficient.

stmt2: f(bx) = 36 = remainder of bx/n. Here, n > 36 and smallest value of bx = 36. Here, we do not know what b is, hence x can be > or < 20. Hence, insufficient.

bigtreezl · Answer

I was guessing A, but couldnt prove it....good soln!

but shouldnt it be n/(x+10) = 42?
and what if n=840 and x=10?

I think I would have ended up marking E

scthakur · Answer

Good point bigtreez!.....my silly mistake. This should be n/(x+10). And, in this case, x+10 > 42 or x > 32. Hence, sufficient. And, if n = 840 and x = 10 then the remainder of n/(x+10) will be 0 and this will not satisfy stmt1.

similarly, from stmt2, n/bx has a remainder of 36 and hence, bx > 36. Here, we do not know b and hence, x. Insufficient.

Answer should still be A.

GMAT TIGER · Answer

but shouldnt it be n/(x+10) = 42?   is not correct. In fact:
n = xk + f(x) whre k is an integer

1: f(x+10) = 42
so x = 32, which is > 20.

2) f(bx) = 36
If x = 1, b is 36 and vicw versa. so not suff.

Also go with A.

amitdgr · Answer

<img src="{SMILIES_PATH}/icon_smile.gif" alt=":)" title="Smile" /> OA is A

icandy · Answer

I agree with the red colored part and the n = xk + f(x)

f(x) = n-kx

f(x+10) = n - k(x+10) = 42

So now how did you deduce that x=32??

amitdgr · Answer

I got this question on my mail, from Princeton .... no idea why they sent me this ... maybe by mistake (I know this is weird ....)

they even had explanation along with this question. The Princeton OE is

1) Only, the remainder is 42, so x+10 must be greater than 42. x+10>42, x>32, x must be greater than 20, sufficient.

2) Only, the same reason as 1), bx>36, we don't know the value of b, so we cannot know if x would be greater than 20 or not, insufficient.

icandy · Answer

I don't get it. What's wrong with me? :shock:

amitdgr · Answer

Precisely why I post this question ... I am not able to understand it .... And now I am confused with all the above posts

Bad question ??

scthakur · Answer

This is a remainder question and simple rule for the remainder question is that the remainder will always be smaller than the divisor. For example, if remainder of x/y is z then z will always be smaller than y.

With this logic, if 42 is the remainder when n is divided by (x+10), then (x+10) > 42 and hence x > 32.

I hope, this is of help.

f(x) is the remainder of n divided by x. If x is a positive

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