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

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A store sells erasers for 0.23$ per piece and pencil for 0.1  [#permalink]

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New post 26 Jul 2014, 10:36
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A
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Difficulty:

  15% (low)

Question Stats:

78% (01:31) correct 22% (00:55) wrong based on 323 sessions

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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$

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Re: A store sells erasers for 0.23$ per piece and pencil for 0.1  [#permalink]

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New post 26 Jul 2014, 10:47
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.
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Re: A store sells erasers for 0.23$ per piece and pencil for 0.1  [#permalink]

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New post 26 Jul 2014, 10:47
Bunuel wrote:
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.


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Hope it helps.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A store sells erasers for 0.23$ per piece and pencil for 0.1  [#permalink]

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New post 21 Mar 2018, 23:11
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 wrote:
Bunuel wrote:
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.


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http://gmatclub.com/forum/joanna-bought ... 01743.html

Hope it helps.
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A store sells erasers for 0.23$ per piece and pencil for 0.1  [#permalink]

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New post 01 Apr 2018, 22:44
honchos wrote:
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$


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
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A store sells erasers for 0.23$ per piece and pencil for 0.1 &nbs [#permalink] 01 Apr 2018, 22:44
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