DS - min and max

Question

Which one .. ?

acfuture · Answer

C

st. 1
we only know c=3, what about the rest of the terms??

st. 2
gives us the rest of the terms to be able to find M-N

M= (largest of x^2)/(smallest of y) +1
N= (smallest of x^2)/(largest of y) +1

sgrover · Answer

(C)

Expression can be rewritten as:
1 + x^2/y

For maxm. value, we will choose max. value of x and min. value of y
For min. value of expression, we will take min. value of x and max. value of y.

N = 1 + a^2/d
M = 1 + b^2/c

M - N =
b^2/c - a^2/d

Require values of a,b,c,d
(C) gives that.

ps_dahiya · Answer

Even though the answer should be C in this case but we should keep the following thing in mind.

Taking the same question:
For the max value of expression we can not take the max value of x because in the main term x is not linear. x is raised to the power two.

I will give you an example.
-5<=x<=1/2
1/2<=y<=1

Take max values of x and y to find M. We get M = 5/4
Take min values of x and y to find N. We get N = 202
Which one is MAX?

If the equation is linear then equation will have max value at the max of all variables and min value at min of all variables.

sharadGmat · Answer

This is really very tricky qn.. Answer is B. Here is the OE: Since X varies from +ve to -ve , the value of x^2 is minimum when x^2 is zero. So Min =N= (0+y)/y=1 Max =M= (5^2+7)/7. So we can find M-N.. :wall

M8 · Answer

Sharad what is the source of your questions?

v1rok · Answer

Hmmm... I disagree with (B). Let me elaborate.

Ok, from Stem2 we know -2<=x<=5 and y<=7.

I agree that Min=N=(0+y)/y=1 happens when x=0

But it is not true that Max=M= (5^2+7)/7=32/7 is the max!

Easy to see: just take y=1, x=5 then M=(25+1)/1=26 (greater than 32/7)

And if you take y=1/2, it will be even larger
And if you take y=0.01, it will be even larger
and so on

The M (Max) will approach infinity as y approaches 0. Since from Stem2 we don't know what the lower limit of y, Max can be anything!

Therefore we can not determine Max-Min from Stem2

In my mind, the answer should be (C).

Anybody agrees?

acfuture · Answer

wow...

i sure did not think that way.... 
yeah, what is the source of the question?

pretty tricky indeed...

v1rok · Answer

yeah, sharad, can you provide the source? I hope that official test writers have much better quality control than some of these shady wanna-learn-how-to-get-700-on-gmat-quick?-then-buy-my-book people...

sharadGmat · Answer

Wow!!! gr8 explanation.. Source is Princeton..In fact I did buy their answer until your post..

sgrover · Answer

Infact, this is also not true ..
If we take -ve values of y, then we can get even less than 1

Try x = -2, y = -8 (since we dont know the lower bound of y)

we get 1/2

I disagree with (B) too.. (C) looks best.

Sharad, please let us know the source of these questions ?

sharadGmat · Answer

Source is Princeton-Quiz book..

Zooroopa · Answer

Good explanation v1rok.

Sharad - Another reason why the OE sounds hollow! In (II) the stem does not specify a non-zero value of 'y'. It simply says c <= y <= 7. Now what happens if c < 0?!! Then y can satisfy zero. This means the expression would become incalculable as division by zero is not defined!

So  B  cannot be the answer.

MA · Answer

also agree with C. nice discussions were found here as well: https://www.gmatclub.com/phpbb/viewtopic ... ht=minimum

v1rok · Answer

Wow! it is the 3rd time in less than a week serious flaws uncovered in materials published by Princeton. (I posted one recently and I also saw another one in my book.) That is just unbelievable! I don't have a lot of confidence in their material anymore

DS - min and max

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