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A store sells five different kinds of nuts. If it is possible to buy

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A store sells five different kinds of nuts. If it is possible to buy  [#permalink]

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New post 06 Feb 2018, 03:20
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

75% (02:20) correct 25% (01:42) wrong based on 36 sessions

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A store sells five different kinds of nuts. If it is possible to buy x pounds of the most expensive nuts for $3.20 and x pounds of the cheapest nuts for $1.40, then which of the following could be the cost of purchasing a mixture containing x pounds of each type of nut?

(A) $1.76

(B) $2.84

(C) $3.54

(D) $13.60

(E) $16.00

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Re: A store sells five different kinds of nuts. If it is possible to buy  [#permalink]

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New post 06 Feb 2018, 03:58
Bunuel wrote:
A store sells five different kinds of nuts. If it is possible to buy x pounds of the most expensive nuts for $3.20 and x pounds of the cheapest nuts for $1.40, then which of
the following could be the cost of purchasing a mixture containing x pounds of each type of nut?

(A) $1.76

(B) $2.84

(C) $3.54

(D) $13.60

(E) $16.00



From a logical standpoint, we can eliminate Options A,B, and C because
if the cheapest nut costs $1.4 and we have to buy x pounds of each of the 5 nuts.

Option E also will not work since the costliest nut will cost $3.2 and all the 5
varieties would need to cost $3.2 for the total cost to be $16.00.

We are left with Option D($13.60) which can be realized by having 3 boxes of the
costliest nut, 1 box of the cheapest nut and one box which costs $2.6.
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Re: A store sells five different kinds of nuts. If it is possible to buy  [#permalink]

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New post 06 Feb 2018, 08:18
Bunuel wrote:
A store sells five different kinds of nuts. If it is possible to buy x pounds of the most expensive nuts for $3.20 and x pounds of the cheapest nuts for $1.40, then which of
the following could be the cost of purchasing a mixture containing x pounds of each type of nut?

(A) $1.76

(B) $2.84

(C) $3.54

(D) $13.60

(E) $16.00


I think this is more of a Logical Question than algebraic.

By looking at the Options only D & E are left. Option E is multiple of most Expensive nuts (i.e. \(3.2 * 5\)), so this Option is ruled out.
Hence, D.
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A store sells five different kinds of nuts. If it is possible to buy  [#permalink]

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New post 06 Feb 2018, 15:13
THIS MIGHT BE INCORRECT but this was my logic.

1) It doesn't matter that there are 5 different nuts, it only matters what the multiples (?) of $3.20 + $1.40 are. Hence quick math...

2) $3.20 + $1.40 = $4.60. (I used 32 + 14 for easy math)

3) I chose a random answer and tried to divide by 4.6 (or 46). [NOT THE MOST TIME EFFICIENT]

4) I chose $13.60 at random because the first three answers are too low.

5) 136/4 = $13.8

6) 20 cents off, I figured it was close enough to $13.6 as the other answers

7) Optional if you have time: I checked $16.00 to see if it would yield one of the answers, it did not

8) D
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Re: A store sells five different kinds of nuts. If it is possible to buy  [#permalink]

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New post 06 Feb 2018, 21:00
1
Bunuel wrote:
A store sells five different kinds of nuts. If it is possible to buy x pounds of the most expensive nuts for $3.20 and x pounds of the cheapest nuts for $1.40, then which of the following could be the cost of purchasing a mixture containing x pounds of each type of nut?

(A) $1.76

(B) $2.84

(C) $3.54

(D) $13.60

(E) $16.00


cost must be>$3.20+4*$1.40=$8.80
cost must be<$1.40+4*$3.20=$14.20
only $13.60 falls within this range
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Re: A store sells five different kinds of nuts. If it is possible to buy  [#permalink]

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New post 08 Feb 2018, 16:38
Bunuel wrote:
A store sells five different kinds of nuts. If it is possible to buy x pounds of the most expensive nuts for $3.20 and x pounds of the cheapest nuts for $1.40, then which of the following could be the cost of purchasing a mixture containing x pounds of each type of nut?

(A) $1.76

(B) $2.84

(C) $3.54

(D) $13.60

(E) $16.00


If each type of the 5 types of nuts is as expensive as the most expensive type of nuts, then x pounds of each type of nuts will cost 5 * $3.20 = $16.00. Similarly, if each type of the 5 types of nuts is as cheap as the cheapest type of nuts, then x pounds of each type of nuts will cost 5 * $1.40 = $7.00. Since not all of the 5 types are as expensive as the most expensive type or as cheap as the cheapest type of nuts, therefore, the cost must be between $7.00 and $16.00. The only number in the answer choices that is between these two amounts is choice D: $13.60.

Answer: D
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Re: A store sells five different kinds of nuts. If it is possible to buy &nbs [#permalink] 08 Feb 2018, 16:38
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