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

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Re: PERCENTAGES - CONCEPTUAL  [#permalink]

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New post 06 Feb 2014, 20:27
3
5
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

74% (03:15) correct 26% (02:45) wrong based on 117 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

Answer (C)

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Re: PERCENTAGES - CONCEPTUAL  [#permalink]

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New post 06 Feb 2014, 20:37
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. :-D :)
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Re: PERCENTAGES - CONCEPTUAL  [#permalink]

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New post 06 Feb 2014, 21:18
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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New post 08 Feb 2014, 01:44
1
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.

Answer: (C)

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

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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New post 03 Aug 2014, 20:55
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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New post 06 Aug 2014, 20:44
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 \(= \frac{3}{\frac{1}{20}} = 20 * 3 = 60\)

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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New post 11 Jan 2017, 07:38
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

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

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New post 12 Jan 2017, 00:15
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


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

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

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New post 12 Jan 2017, 06:39
[/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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Re: Hal bought walnuts at 5 for $1 and apples at 4 for $1.  [#permalink]

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Re: Hal bought walnuts at 5 for $1 and apples at 4 for $1. &nbs [#permalink] 09 Aug 2018, 06:14
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