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# Sally gave some of her candy to her friends. How many pieces

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Director
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Sally gave some of her candy to her friends. How many pieces [#permalink]

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16 Jan 2013, 09:36
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Sally gave some of her candy to her friends. How many pieces of candy did she have before giving any to her friends?

(1) Sally gave each friend 8 pieces of candy
(2) Sally had 7 pieces of candy left after giving candy to her friends.

[Reveal] Spoiler: OA

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Last edited by Bunuel on 16 Jan 2013, 10:06, edited 1 time in total.
Renamed the topic and edited the question.

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Re: Sally gave some of her candy to her friends. How many pieces [#permalink]

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16 Jan 2013, 10:10
Sally gave some of her candy to her friends. How many pieces of candy did she have before giving any to her friends?

(1) Sally gave each friend 8 pieces of candy. Clearly insufficient.

(2) Sally had 7 pieces of candy left after giving candy to her friends. Also insufficient.

(1)+(2) If Sally gave candy to 2 of her friends, then she had 7+2*8=22 pieces of candy but if she gave candy to 3 of her friends, then she had 7+3*8=31 pieces of candy. Not sufficient.

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Re: Sally gave some of her candy to her friends. How many pieces [#permalink]

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16 Jan 2013, 10:18
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Consider X be total number of candies Sally had before giving any to her friend. We need to find X.

1) sally gave each friend 8 pieces of candy
INSUFFICIENT: We dont know number of friends and how many pieces are left after distributing the candies:
If there are 2 friends and 2 candies were left then X = 2*8+2=18
If there are 3 friends and 2 candies were left then X = 3*8+2=26

2) sally had 7 pieces of candy left after giving candy to her friends.
INSUFFICIENT: This choice doesn't tell number of friends and how many pieces she distributed per friend
If there are 2 friends and 1 candy was given per friend then X = 2*1+7= 9
If there are 3 friends and 1 candy was given per friend then X = 3*1+7= 10

Combining (1) & (2): gave each friend 8 pieces of candy & 7 pieces of candy left after distribution:
INSUFFICIENT: Even after combining we dont know the number of friends.
If there are 2 friends then x = 2*8+7= 23
If there are 3 friends then x = 3*8+7= 31

We cannot identify x (No. of pieces of candy Sally has) using any of above statements or combined.

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Re: Sally gave some of her candy to her friends. How many pieces [#permalink]

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16 Jan 2013, 10:48
Statement 1: Could 1 friend, could have 2 friends...etc... Not Sufficient
Statement 2: Same logic as the first statement. Could have given 1 piece of candy out, could have given 2 pieces of candy out..etc.. Not Sufficient.
Statements 1&2 Together: Could have 1 friend (total of 15 pieces of candy), Could have 2 friends (total of 23 pieces of candy)...etc... Not sufficient.
E.

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Re: Sally gave some of her candy to her friends. How many pieces [#permalink]

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16 Jan 2013, 19:59
So basically this question is testing the concept of remainders?
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Re: Sally gave some of her candy to her friends. How many pieces [#permalink]

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16 Jan 2013, 21:09
Yes divisibility & remainders.
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Last edited by PrashantPonde on 16 Jan 2013, 21:27, edited 1 time in total.

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Re: Sally gave some of her candy to her friends. How many pieces [#permalink]

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16 Jan 2013, 21:24
fozzzy wrote:
So basically this question is testing the concept of remainders?

Yes, you can easily express it in remainder terms.

N = QD + R

N - Total candy she had at the beginning
Q - No. of friends (the quotient)
D - No of candies given to each friend (the divisor)
R - No of candies she is left with (the remainder)

To get the value of N, you need to know Q, D and R.
Statement 1 gives you D and statement II gives you R.
You still don't have Q i.e. the number of friends so you cannot find N.

When working on division and remainders, visualize the question in terms of grouping. Check out the division and remainder posts on my blog. (The Veritas site is under maintenance right now so I am unable to give you the links. Just search for 'quarter wit quarter wisdom division' on our blog search)
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Re: Sally gave some of her candy to her friends. How many pieces   [#permalink] 16 Jan 2013, 21:24
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