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# A health food store prepares a breakfast food that consists of oats

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Math Expert
Joined: 02 Sep 2009
Posts: 49540
A health food store prepares a breakfast food that consists of oats  [#permalink]

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12 Jul 2018, 00:57
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Difficulty:

5% (low)

Question Stats:

94% (01:05) correct 6% (01:25) wrong based on 48 sessions

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A health food store prepares a breakfast food that consists of oats, raisins, and nuts mixed in the ratio 9:2:1, respectively, by weight. If the nuts in the mixture weigh 9.2 pounds, how many pounds does the total mixture weigh?

(A) 82.2
(B) 92.2
(C) 101. 2
(D) 110.4
(E) 165.6

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Re: A health food store prepares a breakfast food that consists of oats  [#permalink]

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12 Jul 2018, 01:13
Bunuel wrote:
A health food store prepares a breakfast food that consists of oats, raisins, and nuts mixed in the ratio 9:2:1, respectively, by weight. If the nuts in the mixture weigh 9.2 pounds, how many pounds does the total mixture weigh?

(A) 82.2
(B) 92.2
(C) 101. 2
(D) 110.4
(E) 165.6

As our numbers our non-integers, before explicitly calculating we'll first try estimating.
This is an Alternative approach.

Since the nuts are 1 ratio unit out of 9 + 2 + 1 = 11 ratio units, an exact answer is (9.2/1) * 11 = 9.2 *11. This is a little bit more than 9 * 11 = 99.

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A health food store prepares a breakfast food that consists of oats  [#permalink]

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12 Jul 2018, 05:25
Bunuel wrote:
A health food store prepares a breakfast food that consists of oats, raisins, and nuts mixed in the ratio 9:2:1, respectively, by weight. If the nuts in the mixture weigh 9.2 pounds, how many pounds does the total mixture weigh?

(A) 82.2
(B) 92.2
(C) 101. 2
(D) 110.4
(E) 165.6

Ratio of Oats : raisins : nuts = 9 : 2 : 1

Total = 12 ( sum of the ratio)

It's given that nuts is mixture weigh 9.2 pounds.

let's assume ,

oats = 9x
raisins = 2x
nuts = x

(9.2 / x) *12x ................if x represents 9.2 pounds , we can also find what 12 x represents.

= 110.4

The best answer is D .
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Joined: 13 Feb 2018
Posts: 130
Re: A health food store prepares a breakfast food that consists of oats  [#permalink]

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12 Jul 2018, 05:33
DavidTutorexamPAL wrote:
Bunuel wrote:
A health food store prepares a breakfast food that consists of oats, raisins, and nuts mixed in the ratio 9:2:1, respectively, by weight. If the nuts in the mixture weigh 9.2 pounds, how many pounds does the total mixture weigh?

(A) 82.2
(B) 92.2
(C) 101. 2
(D) 110.4
(E) 165.6

As our numbers our non-integers, before explicitly calculating we'll first try estimating.
This is an Alternative approach.

Since the nuts are 1 ratio unit out of 9 + 2 + 1 = 11 ratio units, an exact answer is (9.2/1) * 11 = 9.2 *11. This is a little bit more than 9 * 11 = 99.

A bit miscalculation

In My Opinion
Ans: D
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2015
Re: A health food store prepares a breakfast food that consists of oats  [#permalink]

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12 Jul 2018, 05:58

Solution

Given:

• Food contain oats, raisins, and nuts in the ratio= 9:2:1 by weight.
• Nuts in the mixture weigh 9.2 pounds

To find:

• How many pounds does the total mixture weigh?

Approach and Working:

Let us assume that weight of nuts in the mixture is x pounds, then the weight of the mixture is 12 x.
• x=9.2 pound
• 12x= 110.4 pounds
Hence, the correct answer is option D.

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Re: A health food store prepares a breakfast food that consists of oats  [#permalink]

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12 Jul 2018, 08:13
Bunuel wrote:
A health food store prepares a breakfast food that consists of oats, raisins, and nuts mixed in the ratio 9:2:1, respectively, by weight. If the nuts in the mixture weigh 9.2 pounds, how many pounds does the total mixture weigh?

(A) 82.2
(B) 92.2
(C) 101. 2
(D) 110.4
(E) 165.6

Nuts weigh 9.20 pounds so the total weight of the mixture is ( 9+2+1 )* 9.20 = 110.4 pounds, Answer must be (D)
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Re: A health food store prepares a breakfast food that consists of oats  [#permalink]

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12 Jul 2018, 09:52
Bunuel wrote:
A health food store prepares a breakfast food that consists of oats, raisins, and nuts mixed in the ratio 9:2:1, respectively, by weight. If the nuts in the mixture weigh 9.2 pounds, how many pounds does the total mixture weigh?

(A) 82.2
(B) 92.2
(C) 101. 2
(D) 110.4
(E) 165.6

O:R:N=9:2:1 = O:R:9.2 = 9x:2x:x
so if x is 9.2, (9+2+1) x or $$12x = 9.2*12$$

Ofcourse the question now is all about doing fast calculations.
Choices can help as answer is NOT approximate but exact

ways this can be done faster

1) TENTHs/last digit -
last digit of the product will be 2*2 = 4
Only D has a 4

2) DIVISIBILITY by 4 and 3
9.2 is not a multiple of 3 but 12 is multiple of 3
so the product 9.2*12 should be a multiple of 3 and 4 but not of 9
(A) 82.2... last two digits are 22 : not div by 4
(B) 92.2 ... 9+2+2=13 : not div by 3
(C) 101. 2.. 1+1+2=4 : not div by 3
(D) 110.4... 1+1+4 = 6 : div by 3 .. and 04 is div by 4.. HENCE our answer
(E) 165.6 ... 1+6+5+6=18: Div by 3 but also by 9

D
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Re: A health food store prepares a breakfast food that consists of oats &nbs [#permalink] 12 Jul 2018, 09:52
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