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

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Manager
Joined: 03 Mar 2018
Posts: 204
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. Manager Joined: 30 Mar 2017 Posts: 123 GMAT 1: 200 Q1 V1 Re: A shopkeeper sells apples for$7 each and strawberries for $15.00 each [#permalink] ### Show Tags 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.

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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, 13:54
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) _________________ You've got what it takes, but it will take everything you've got Retired Moderator Joined: 27 Oct 2017 Posts: 1273 Location: India Concentration: International Business, General Management GPA: 3.64 WE: Business Development (Energy and Utilities) Re: A shopkeeper sells apples for$7 each and strawberries for $15.00 each [#permalink] ### Show Tags 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. hence answer B Posted from my mobile device Posted from my mobile device _________________ e-GMAT Representative Joined: 04 Jan 2015 Posts: 3142 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.

_________________

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
Joined: 30 Mar 2017
Posts: 123
GMAT 1: 200 Q1 V1
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.