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# A shopkeeper sells apples for $7 each and strawberries for$15.00 each

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A shopkeeper sells apples for $7 each and strawberries for$15.00 each  [#permalink]

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20 Mar 2018, 13:16
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Difficulty:

55% (hard)

Question Stats:

63% (01:36) correct 37% (01:04) wrong based on 76 sessions

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A shopkeeper sells apples for $7 each and strawberries for$15.00 each. How many apples did the shopkeeper sell today?

(1) The number of apples sold today is 1 more than twice the number of strawberries sold.
(2) Today the shopkeeper received a total of $65 from the sale of both apples and strawberries. _________________ Please mention my name in your valuable replies. Senior PS Moderator Joined: 26 Feb 2016 Posts: 3333 Location: India GPA: 3.12 A shopkeeper sells apples for$7 each and strawberries for $15.00 each [#permalink] ### Show Tags 20 Mar 2018, 13:54 itisSheldon wrote: A shopkeeper sells apples for$7 each and strawberries for $15.00 each. How many apples did the shopkeeper sell today? (1) The number of apples sold today is 1 more than twice the number of strawberries sold. (2) Today the shopkeeper received a total of$65 from the sale of both apples and strawberries.

Let A be the number of apples and S the number of strawberries

1. A = 2S + 1

If S = 1, A = 2+1 = 3
If S = 2, A = 4+1 = 5
We cannot find a unique value for the number of apples sold.(Insuffiicient)

2. 7A + 15S = 65

This is only possible when A = 5, S = 2 since both
apples and strawberries are sold (Sufficient - Option B)
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Re: A shopkeeper sells apples for $7 each and strawberries for$15.00 each  [#permalink]

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20 Mar 2018, 18:16
St1: no of apple = 2* number of strawberry +1. No other info . Hence insufficient.
St2:7x+5y=65. Since the number of fruits can only be POSITIVE INTEGER, hence finding integer solution, we get apple =5, and strawberry=2 is the only INTEGER solution.sufficient.

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Re: A shopkeeper sells apples for $7 each and strawberries for$15.00 each  [#permalink]

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21 Mar 2018, 10:07
1
Let x = # of apples sold
Let y = # of strawberries sold

Statement 1, represented as an equation is
$$x = y + 1$$
Clearly not sufficient, since we have 1 linear equation with 2 unknowns.

Statement 2, represented as an equation is
$$7x + 15y = 65$$

It's very tempting to immediately choose Answer C since we have 2 equations with 2 unknowns, but this is a trap. Let's see what possible values of x and y would fit the equation...
Note that we can't have x=0 or y=0 because neither 7 is factor of 65, nor 15 is a factor of 65. And since we're dealing with # of fruit, x and y must be some positive integers.

Let's take $$7x$$ first. It's obvious that $$65$$ is a multiple of 5 and $$15y$$ is a multiple of 5. Thus, $$7x$$ must be a multiple of 5. So x can equal {5,10,15,etc}. However if x=10, then 7x=70, which means we won't have a positive value for y. So x=5 is the only possible value for x. Substituting x=5 into the equation and solving for y we get:
$$7x + 15y = 65$$
$$7(5) + 15y = 65$$
$$15y = 30$$
$$y = 2$$

Thus, selling 5 apples and 2 strawberries is the only way the shopkeeper could have received $65. Sufficient. Answer: B e-GMAT Representative Joined: 04 Jan 2015 Posts: 3085 A shopkeeper sells apples for$7 each and strawberries for $15.00 each [#permalink] ### Show Tags Updated on: 24 Mar 2018, 17:32 Solution Let the number of apples sold today be ‘$$a$$’ and the number of strawberries sold today be ‘$$b$$’. Statement-1The number of apples sold today is $$1$$more than twice the number of strawberries sold “. • $$a = 2b+1$$ The above expression does not give any information about the value of the number of apples sold today. Hence, Statement 1 alone is not sufficient to answer the question. Statement-2Today the shopkeeper received a total of$$$65$$ from the sale of both apples and strawberries.

• $$7a+15b=65$$
• $$15b$$ ends either with a zero or 5.
•Thus, for $$7a+15b$$ to end with a $$5$$, $$7a$$ must end either with the $$5$$ or $$0$$.
• The only possible value of ‘$$a$$’ and ‘$$b$$’ is $$5$$ and $$2$$ respectively.

Hence, Statement 2 alone is sufficient to answer the question.

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Originally posted by EgmatQuantExpert on 24 Mar 2018, 14:55.
Last edited by EgmatQuantExpert on 24 Mar 2018, 17:32, edited 3 times in total.
Manager
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Re: A shopkeeper sells apples for $7 each and strawberries for$15.00 each  [#permalink]

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24 Mar 2018, 15:07
EgmatQuantExpert wrote:

Solution

Let the number of apples sold today be ‘$$a$$’ and the number of strawberries sold today be ‘$$b$$’.

Statement-1The number of apples sold today is $$1$$more than twice the number of strawberries sold “.

• $$a = 2b+1$$

The above expression does not give any information about the value of the number of apples sold today.

Hence, Statement 1 alone is not sufficient to answer the question.