NoteBook & Markers

[gmat740]

At a certain bookstore, each notepad costs x dollars and each markers costs y dollars. If $10 is enough to buy 5 notepads and 3 markers, is $10 enough to buy 4 notepads and 4 markers instead?

1). each notepad cost less than $1

2). $10 is enough to buy 11 notepads

OA-E

My Approach :

Given : 5x +3y <10
to find : 4x + 4y <10
= 4(x +y) <10

1. x<1(Insuff)
2. 10y< 11 => y< 1.1

Now combine both

We take the max possible value i.e x=1(although equality does not exists,but just for the sake of easy calculations)

and max of y from (2) => y=1.1

Now put this in the expression :
4(x + y) = 4*(1 +1.1) = 4*2.1 = 8.4 <10

so even if we take both the max value of x and y, we still have sufficient money to buy 4x and 4y within $10
so IMO-C

This is a GMAT Prep Question. So the OA is correct. Please tell me where am I wrong.

Thanks

[zenithexe]

hmm, from my calculations,

the max value of X would be 10/11 when considering both restrictions.
Plug that number in 5X+3Y<=10 we get max value of Y to be 20/11,

plug it in to 4X+4Y, we get 120/11 or 10.91, (greater than 110/11)
of course, the values of X and Y can lower, so we don't know if $10 is enough to by 4 of each.

We take the max possible value i.e x=1(although equality does not exists,but just for the sake of easy calculations)

I think that's where your answer goes wrong, the max value of X is 10/11

[ssmiles08]

I think you are using x as notepads and y as markers. But both choices here are giving the value of notepads. The value of markers can be anything. which could make the value > 10.

IMO your equation 4(x + y) = 4*(1 +1.1) = 4*2.1 = 8.4 <10 is wrong.

-Hope this helps.

[PussInBoots]

1). each notepad cost less than $1

2). $10 is enough to buy 11 notepads

Are you sure these are correct? If so, answer is indeed E because we dont know anything about markers. For all we know notepads could cost 1 cent while markers $3/each.

[ymach3]

Yes, i agree with PussInBoots....


(correct idiom usage - "agree with (a person/idea)"
agree to (plan/action))

Please dont mind bringing in idoms to Math..