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# Two varieties of steel, A and B, have a ratio of iron to chromium as 5

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Intern
Joined: 05 Aug 2014
Posts: 30

Kudos [?]: 82 [2], given: 24

Two varieties of steel, A and B, have a ratio of iron to chromium as 5 [#permalink]

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24 May 2015, 08:03
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Difficulty:

55% (hard)

Question Stats:

69% (02:01) correct 31% (02:25) wrong based on 185 sessions

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Two varieties of steel, A and B, have a ratio of iron to chromium as 5:1 and 7:2, respectively. Steel C is produced by mixing alloys A and B at a ratio of 3:2. What is the ratio of iron to chromium in C?

(A) 17 : 73
(B) 78 : 14
(C) 45 : 30
(D) 73 : 17
(E) 4 : 9

[Reveal] Spoiler: OA

Kudos [?]: 82 [2], given: 24

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

Kudos [?]: 2085 [2], given: 6

Re: Two varieties of steel, A and B, have a ratio of iron to chromium as 5 [#permalink]

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24 May 2015, 08:35
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In 6 parts of alloy A, 5 parts are iron, and 1 part is chromium.

In 9 parts of alloy B, 7 parts are iron and 2 parts are chromium.

First, to compare the two alloys, get the same number of parts in total - we can use 18. So we have:

In 18 parts of alloy A, 15 parts are iron and 3 are chromium.
In 18 parts of alloy B, 14 parts are iron and 4 are chromium.

So combining 3 of A with 2 of B, we'd be combining 45 and 28 parts of iron, or 73 parts of iron, with 9 and 8 of chromium, or 17 of chromium, so 73 to 17 is the answer.
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Kudos [?]: 2085 [2], given: 6

Director
Joined: 07 Aug 2011
Posts: 579

Kudos [?]: 608 [0], given: 75

GMAT 1: 630 Q49 V27
Two varieties of steel, A and B, have a ratio of iron to chromium as 5 [#permalink]

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24 May 2015, 11:12
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naeln wrote:
Two varieties of steel, A and B, have a ratio of iron to chromium as 5:1 and 7:2, respectively. Steel C is produced by mixing alloys A and B at a ratio of 3:2. What is the ratio of iron to chromium in C?

(A) 17 : 73
(B) 78 : 14
(C) 45 : 30
(D) 73 : 17
(E) 4 : 9

Such questions test your knowledge on weighted average concept . Initially this technique may seem daunting but once you get familiar , you will find this technique very useful on GMAT.

Ok , so for this question we can focus on either Iron or chromium to get to the solution . i will show both ways .

in A , Iron = 5/6
in B , Iron= 7/9
resultant mixture has 3 portions of A for every 2 portions of B , so weighted average of Iron will lie closer to A than to B .
Specifically , w.Avg (Iron) in mixture will be 2 portion away from A and 3 portion away from B as shown in picture.
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Kudos [?]: 608 [0], given: 75

Director
Joined: 07 Dec 2014
Posts: 884

Kudos [?]: 308 [1], given: 17

Two varieties of steel, A and B, have a ratio of iron to chromium as 5 [#permalink]

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08 Apr 2016, 10:50
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iron in 3A+2B=3(5/6)+2(7/9)=73/18
chromium in 3A+2B=3(1/6)+2(2/9)=17/18
iron:chromium ratio in C=(73/18)/(17/18)=73/17

Kudos [?]: 308 [1], given: 17

Retired Moderator
Joined: 23 Sep 2015
Posts: 401

Kudos [?]: 99 [2], given: 72

Location: France
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)
Re: Two varieties of steel, A and B, have a ratio of iron to chromium as 5 [#permalink]

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23 Apr 2016, 03:33
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Finding the weighted average of one of the two :
Iron:
In solution A iron is 5/6
In solution B iron is 7/9

The ratio for Solution C is 3:2 for A and B respectively. This means that 60% of A was used and 40% of B

To find the weight of iron in the new solution: we do the weighted average:

$$\frac{5}{6}*\frac{3}{5}+\frac{7}{9}*\frac{2}{5}$$

We get $$\frac{73}{90}$$

73 is the weight of Iron and 90 is total
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Kudos [?]: 99 [2], given: 72

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Kudos [?]: 291 [0], given: 0

Re: Two varieties of steel, A and B, have a ratio of iron to chromium as 5 [#permalink]

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05 Sep 2017, 18:27
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Re: Two varieties of steel, A and B, have a ratio of iron to chromium as 5   [#permalink] 05 Sep 2017, 18:27
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