A store sells erasers for 0.23$ per piece and pencil for 0.1

Question

A store sells erasers for 0.23$ per piece and pencil for 0.11$ per piece. How many eraser and pencils did Jessica buy?

(1) She bough 5 erasers 
(2) She spent total of 1.70$

Bunuel · Accepted Answer

Similar questions to practice: eunice-sold-several-cakes-if-each-cake-sold-for-either-109602.html martha-bought-several-pencils-if-each-pencil-was-either-a-100204.html a-rental-car-agency-purchases-fleet-vehicles-in-two-sizes-a-105682.html joe-bought-only-twenty-cent-stamps-and-thirty-cent-stamps-106212.html a-certain-fruit-stand-sold-apples-for-0-70-each-and-bananas-101966.html joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html Hope it helps.

munchkin123 · Answer

Trial and error is too long and is not exhaustive enough.

There is a simpler solution.

Now, we know that 23x + 11y = 170

The units digit of 23 and 11 should add up to a 0.

So taking the units digit only ->

23x --> 3, 6, 9, 2, 5, 8, 1, 4, 7, 0
11y --> 1, 2, 3, 4, 5, 6, 7, 8, 9, 0

There are a lot of combinations, but trying the easiest first helps ->
(0,0) 
23*10 + 11*10 = 340 !! (Voila) This is exactly double of what we need. Halve it.

So, x and y are 5 each.

(Cross checking with Option 1, we see that x is 5 is given, so we can be sure that this is the only answer)

Takes 45 seconds.

But, to be doubly sure, take some other combination in random, Say, (6, 4)

23*2 + 11*4 = 46 + 44 = 90 (Too low)

A bit higher is (5,5), almost confirmed. Have a leap of faith and mark B.

Bunuel · Answer

A store sells erasers for 0.23$ per piece and pencil for 0.11$ per piece. How many eraser and pencils did Jessica buy?

(1) She bough 5 erasers. Clearly insufficient.

(2) She spent total of 1.70$ -->  0.23e+0.11p=1.70  -->  23e+11p=170  --> by trial and error we can find that the only non-negative integer solution for this equation is e=5 and p=5. Sufficient.

Answer: B.

DhruvPatelD10 · Answer

Given : P(Eraser) = 0.23 , P(Pencil) = 0,11
To find No. of Erasers and No. of Pencils

Statement 1 : 
 No of erasers = 5 , nut we cannot get the No of pencils -->  Insufficient

Statement 2 : 
 1.70 = 0.23*E + 0.11*P , we don't know values of E and P -->  Sufficient 
Plus , E and P > 0
E = 5 P = 5

Option B

kitipriyanka · Answer

A. NO info about pencils. Insufficient
B. only 5 erasers and 5 pencil satisfy the equation : 0.23e+0.11p=1.70

Hence B

TheNightKing · Answer

Hello  Bunuel  Sir, 
Will it be right to say that since 23 and 11 are co-prime hence there will be only one unique solution and hence sufficient?

RiRa777 · Answer

Hi,

I see that in questions of similar types, all the explanations involve a trial and error method. I was wondering if there is a way to be sure that the result we stumble upon is actually the only possible combination. Even if I arrive at integer values that fit the equation, I still need to check that other numbers don't. And this process always takes more than the allotted time for a question(2 mins). I would be glad if anyone can help me with a way to ensure that no other solution exist once I arrive at a solution, that would save some precious seconds.

Thank you!

Danchar42 · Answer

I was really excited to see this comment! I thought it'd be a nice trick, but after testing it out I'm not sure it works, even in best-case scenario. I'm curious to hear other thoughts, because I may be mis-understanding.

let's say erasers are 0.03, and pencils are 0.05, and the total bill was 1.50
 e.g.
rearrange to get 3E + 5P = 150
3 and 5 are co-prime, as in the OP question
several solutions exist (E=5 & P=27, or E=10 & P=24, etc.)

When if 3*5 is NOT a multiple of the total price, then is still doesn't work
 e.g.
3E + 5P = 160
multiple solutions still exist (E=5 & P=29, or E=10 and P=26)

Even if the individual prices are not factors in the total bill, then I think the trick about them being "co-prime is sufficient" still does not work
 e.g.
3E + 5P = 112 (which = 2^4*7)
multiple solutions still exist (E=34 & P=2, or E=9 and P=17)

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.

A store sells erasers for 0.23$ per piece and pencil for 0.1

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

A store sells erasers for 0.23$ per piece and pencil for 0.1

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