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• ### $450 Tuition Credit & Official CAT Packs FREE January 15, 2019 January 15, 2019 10:00 PM PST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### The winning strategy for a high GRE score January 17, 2019 January 17, 2019 08:00 AM PST 09:00 AM PST Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. # A shopkeeper sells apples for$7 each and strawberries for $15.00 each  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 03 Mar 2018 Posts: 215 A shopkeeper sells apples for$7 each and strawberries for $15.00 each [#permalink] ### Show Tags 20 Mar 2018, 12:16 1 00:00 Difficulty: 55% (hard) Question Stats: 62% (01:37) correct 38% (01:06) wrong based on 73 sessions ### HideShow timer Statistics 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.

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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, 12:54
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 Senior DS Moderator Joined: 27 Oct 2017 Posts: 1195 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, 17:16 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 _________________ Manager Joined: 30 Mar 2017 Posts: 134 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, 09:07 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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Updated on: 24 Mar 2018, 16:32

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. Answer: B _________________ Register for free sessions Number Properties | Algebra |Quant Workshop Success Stories Guillermo's Success Story | Carrie's Success Story Ace GMAT quant Articles and Question to reach Q51 | Question of the week Must Read Articles Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2 Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2 Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry Algebra- Wavy line | Inequalities Practice Questions Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets | '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com Originally posted by EgmatQuantExpert on 24 Mar 2018, 13:55. Last edited by EgmatQuantExpert on 24 Mar 2018, 16:32, edited 3 times in total. Manager Joined: 30 Mar 2017 Posts: 134 GMAT 1: 200 Q1 V1 Re: A shopkeeper sells apples for$7 each and strawberries for $15.00 each [#permalink] ### Show Tags 24 Mar 2018, 14:07 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. Statement-2Today the shopkeeper received a total of$$$65$$ from the sale of both apples and strawberries.

• $$7a+10b=65$$
• $$10b$$ always ends with a zero.
•Thus, for $$7a+10b$$ to end with a $$5$$, $$7a$$ must end with the $$5$$.
• The only possible value of ‘$$a$$’ and ‘$$b$$’ is $$5$$ and $$3$$ respectively.

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

Re statement 2, strawberries cost $15 each, not$10 each.
Re: A shopkeeper sells apples for $7 each and strawberries for$15.00 each &nbs [#permalink] 24 Mar 2018, 14:07
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