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# Hal bought walnuts at 5 for $1 and apples at 4 for$1.

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
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06 Feb 2014, 21:27
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45% (medium)

Question Stats:

71% (03:08) correct 29% (02:52) wrong based on 120 sessions

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aimlockfire1 wrote:
Hal bought walnuts at 5 for $1 and apples at 4 for$1.He spent a total of $19.50 . He sells both at 20 for$5 and as a result gains $3 .How many walnuts did Hal buy ? a)50 b)45 c)60 d)80 e)55 Let's start with the concrete information: He buys everything for$19.50 and earns $3 after selling so he sells everything for$22.50 (= 2250 cents).
He sells each item for 5/20 = 25 cents so in all he sells 2250/25 = 90 items

Cost of each walnut = 1/5 = $.2 = 20 cents Cost of each apple = 1/4 =$.25 = 25 cents

Now we have one equation to solve:
20*w + 25*(90 - w) = 1950 (w is the number of walnuts he buys)
4w + 5(90 - w) = 390
w = 60

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06 Feb 2014, 21:37
aimlockfire1 wrote:
Hal bought walnuts at 5 for $1 and apples at 4 for$1.He spent a total of $19.50 . He sells both at 20 for$5 and as a result gains $3 .How many walnuts did Hal buy ? a)50 b)45 c)60 d)80 e)55 Let me try this, 5 for$1 and apples at 4 for $1.He spent a total of$19.50 this statement clearly tells that for 0.5 he buys apple(So that quantity can be integer.

Lets go with options : 50 walnuts
10$Remaining amount -- 9.5 so total apple he buys = 38 total items 50+38 =88 he sells 20 for 5$ mean 4 for 1$.So he earns == 22 dollors Diffrence 22-19.5 == 2.5 -- Wrong Answer. 2nd options 45 walnuts, 9$ for walnuts
10.5$for apple 42 apple. so total quantity == 87 if he sells 4 for 1$. 21.75 == Diffrence less than 3$. 3rd choice, 60 walnuts, 12$ for walnuts.
7.5$for apple -- 30 apples. total 90 if he sells 4 for 1$. 22.5so diffrence == 3$. 4th choice, 80 walnuts, 16$ for walnuts
3.5 for apples 14 apples. 94 total. if sells at 4 per 1$. 23.5 diffrence greater than 3. 5th choice 55 walnuts 11$ for walnuts.
8.5 for apples, 34 apples. 89 in total. if sells at 4 per 1$. 22.15 diffrence less than 3. So correct choice is C. Retired Moderator Joined: 20 Dec 2013 Posts: 166 Location: United States (NY) GMAT 1: 640 Q44 V34 GMAT 2: 710 Q48 V40 GMAT 3: 720 Q49 V40 GPA: 3.16 WE: Consulting (Venture Capital) Re: PERCENTAGES - CONCEPTUAL [#permalink] ### Show Tags 06 Feb 2014, 22:18 2 Haven't seen too many like this, but given he pays 20cts per walnut and 25cts per apple and sells each at 25cts, he actually makes no profit/loss on the apples, and so they become irrelevant to determine his profit of$3 (as does his cost basis of $19.50, because there is only one possible way for him to profit exactly$3).

@5cts profit per walnut, just need to calculate 3/.05 = 60
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Re: Hal bought walnuts at 5 for $1 and apples at 4 for$1.  [#permalink]

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08 Feb 2014, 02:44
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Hal bought walnuts at 5 for $1 and apples at 4 for$1. He spent a total of $19.50 . He sells both at 20 for$5 and as a result gains $3 .How many walnuts did Hal buy ? A. 50 B. 45 C. 60 D. 80 E. 55 Method 1: Number of Walnuts=W Number of Apples = A Given that, Hal bought walnuts at 5 for$1 and apples at 4 for $1 and he spent a total of$19.50

So, $$\frac{W}{5} + \frac{A}{4}=19.5$$ .......(1)

Given that, Hal sells both at 20 for $5 and as a result gains$3

So, $$(\frac{W}{20})*5 + (\frac{A}{20})*4 = 19.5 + 3$$

Or, $$\frac{W}{4} +\frac{A}{4}= 22.5$$ .......(2)

Solving (1) & (2), we get number of walnuts W as 60.

Method 2:

Given that, Hal bought walnuts at 5 for $1 and apples at 4 for$1.
Hence, buying price of walnut = 20 cents; buying price of apple = 25 cents

Given that, Hal sells both at 20 for $5 and as a result gains$3
Selling price of walnut or apple= $5/20 = 25 cents Since, buying and selling price of apple is same, the profit of$3 is made by selling only walnut.
Profit from selling 1 walnut = (25 - 20 )cents= 5 cents
Number of walnut sold to get $3 profit = ($3)/(5 cents) = 60

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Re: Hal bought walnuts at 5 for $1 and apples at 4 for$1.  [#permalink]

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03 Aug 2014, 21:55
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He buys walnuts at a price of 20 cents each and apples at a price of 25 cents each. He then sells both of them at 25 cent each. This means that the 3$profit he made result only from the walnuts. Hence: Profit = 3$ = 300 cents / 5 cents = 60.

He bought 60 walnuts. Answer C.
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Re: Hal bought walnuts at 5 for $1 and apples at 4 for$1.  [#permalink]

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06 Aug 2014, 21:44
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Just look at the cost price & selling price of apples. They are same; so no profit is booked by them

They can be ignored in equation formation (One variable less )

Cost price of 1 walnut $$= \frac{1}{5}$$

Sell price of 1 walnut$$= \frac{1}{4}$$

Profit on 1 walnut$$= \frac{1}{4} - \frac{1}{5} = \frac{1}{20}$$

Total profit earned = 3

So, no. of walnuts sold $$= \frac{3}{\frac{1}{20}} = 20 * 3 = 60$$

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Re: Hal bought walnuts at 5 for $1 and apples at 4 for$1.  [#permalink]

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11 Jan 2017, 08:38
VeritasPrepKarishma wrote:
aimlockfire1 wrote:
Hal bought walnuts at 5 for $1 and apples at 4 for$1.He spent a total of $19.50 . He sells both at 20 for$5 and as a result gains $3 .How many walnuts did Hal buy ? a)50 b)45 c)60 d)80 e)55 Let's start with the concrete information: He buys everything for$19.50 and earns $3 after selling so he sells everything for$22.50 (= 2250 cents).
He sells each item for 5/20 = 25 cents so in all he sells 2250/25 = 90 items

Cost of each walnut = 1/5 = $.2 = 20 cents Cost of each apple = 1/4 =$.25 = 25 cents

Now we have one equation to solve:
20*w + 25*(90 - w) = 1950 (w is the number of walnuts he buys)
4w + 5(90 - w) = 390
w = 60

I don't think the question is clearly stated. "Hal bought walnuts at 5 for $1" is it sufficiently clear? what source is the question from? are you posting an official question? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 9697 Location: Pune, India Re: Hal bought walnuts at 5 for$1 and apples at 4 for $1. [#permalink] ### Show Tags 12 Jan 2017, 01:15 hongson1706 wrote: VeritasPrepKarishma wrote: aimlockfire1 wrote: Hal bought walnuts at 5 for$1 and apples at 4 for $1.He spent a total of$19.50 . He sells both at 20 for $5 and as a result gains$3 .How many walnuts did Hal buy ?

a)50

b)45

c)60

d)80

e)55

He buys everything for $19.50 and earns$3 after selling so he sells everything for $22.50 (= 2250 cents). He sells each item for 5/20 = 25 cents so in all he sells 2250/25 = 90 items Cost of each walnut = 1/5 =$.2 = 20 cents
Cost of each apple = 1/4 = $.25 = 25 cents Now we have one equation to solve: 20*w + 25*(90 - w) = 1950 (w is the number of walnuts he buys) 4w + 5(90 - w) = 390 w = 60 Answer (C) I don't think the question is clearly stated. "Hal bought walnuts at 5 for$1" is it sufficiently clear? what source is the question from? are you posting an official question?

Yes, the rate is given. It could be in terms of $/cents per walnut or no. of walnuts per dollar. There shouldn't be a problem here. _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Intern Joined: 30 Nov 2016 Posts: 15 Re: Hal bought walnuts at 5 for$1 and apples at 4 for $1. [#permalink] ### Show Tags 12 Jan 2017, 07:39 [/quote] Yes, the rate is given. It could be in terms of$/cents per walnut or no. of walnuts per dollar. There shouldn't be a problem here.[/quote]
it should be more clearly stated, "Hal bought 5 walnuts for $1", if you say "Hal bought walnuts at 5 for$1", is it correctly written in formal English? honestly I've never seen such an idiom.
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Hal bought walnuts at 5 for $1 and apples at 4 for$1.  [#permalink]

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30 May 2019, 07:53
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Each walnut costs: 20 c
Each apple costs: 25 c

At the time of selling
Each item sells at: 500/20 --> 25 c
So, in a way, no profit is being earned on selling apples. CP=SP
So, the total profit of 300 c is being earned on selling walnuts.
Profit on each walnut= 25-20=5c
No. of walnuts=Total profit/ profit on each walnut=300/5=60
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Re: Hal bought walnuts at 5 for $1 and apples at 4 for$1.  [#permalink]

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30 May 2019, 08:21
The word'both' is misleading in this question. It should have been 'each'

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Re: Hal bought walnuts at 5 for $1 and apples at 4 for$1.  [#permalink]

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31 May 2019, 00:27
I answered this question in 2:09 using plug in numbers. It felt the easiest and most tangible. I began with 5/$1= 20 cents/walnut and 4/$1 = 25 cent apples. I then took the total of $19.50 and added the profit of$3 to it to get $22.50. From there I began with answer choice C to see what answer I would get. - 60 walnuts * 20 cents each is$12.
- I know he spent $19.50 so I took 19.5-12=7.5 - Then I used that$7.50 towards apples. 7.50/25. (Or in this case, for quick math, I did 4 per dollar so 4x7=28+2=30 (the extra +2 was for the 50 cents))