If goods be purchased for 840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
A. 30%
B. 33%
C. 33 1/3%
D. 35%
[ please help me to understand similar maths with a simple and short formula ]
THANKS IN ADVANCE.
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If goods be purchased for 840
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DavidG@VeritasPrep
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We're missing an answer choice here, but...emdadul28 wrote:If goods be purchased for 840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
A. 30%
B. 33%
C. 33 1/3%
D. 35%
[ please help me to understand similar maths with a simple and short formula ]
THANKS IN ADVANCE.
Let's say there are 84 items purchased at $10 each. If we want a 20% profit, we'll need to make 20% of 840, or $168, so we'll require 840 + 168 = $1008 total revenue.
If 1/4 of the items were sold for a loss of 20%, each of these items was sold for $8. 1/4 of 84 is 21; these 21 items will bring in 8*21 = 168.
If we need total revenue of 1008, and we've brought in $168 with the first 21 items sold, that means the remaining 63 items will need to bring in another $840. So these items will need to go for 840/63, or 40/3 = 13 1/3 each.
If we purchased those items at $10 and sold them for 13 1/3, we'll make a profit of 3 1/3, or 33 1/3%. The answer is C
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DavidG@VeritasPrep
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And if you're more of an allegation type of person, think of it this way. 1/4 of the items returned a profit of -20%. the overall profit should be 20%. So we're trying to determine what profit the other 3/4 of the items should return. If 1/4 of the items yielded a loss and 3/4 yielded a profit, then the number of items yielding a profit was three times as many as the number that returned a loss. Thus that 3:1 (or 3x:x) gap will help us conceptualize the distance of each group from the overall average.emdadul28 wrote:If goods be purchased for 840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
A. 30%
B. 33%
C. 33 1/3%
D. 35%
[ please help me to understand similar maths with a simple and short formula ]
THANKS IN ADVANCE.
-20----------------20-------?
Gap:-------3x-----------x----
If 3x represents the distance between -20 and 20, then 3x = 40, and x = 40/3, or 13 1/3.
20 + x = 13 1/3 = 33 1/3. The answer is C
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[email protected]
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Hi emdadul28,
To start, what is the source of this question? I ask because it's not worded in proper GMAT 'style' and it does not include 5 answer choices. If you're actually studying for the GMAT, then you might want to invest in more realistic, reputable practice materials.
That having been said, the basic premise of this question can be dealt with algebraically. 1/4 of 840 = 210, so 210 of the goods are sold at a 20% loss and the remaining 630 of the goods will be sold at an X% gain so that the OVERALL gain will be 20%. That information can be translated into the following equation:
210(.8) + 630(X) = 840(1.2)
168 + 630X = 1008
630X = 840
X = 840/630 = 280/210 = 4/3
4/3 would be a 33.3333% gain.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
To start, what is the source of this question? I ask because it's not worded in proper GMAT 'style' and it does not include 5 answer choices. If you're actually studying for the GMAT, then you might want to invest in more realistic, reputable practice materials.
That having been said, the basic premise of this question can be dealt with algebraically. 1/4 of 840 = 210, so 210 of the goods are sold at a 20% loss and the remaining 630 of the goods will be sold at an X% gain so that the OVERALL gain will be 20%. That information can be translated into the following equation:
210(.8) + 630(X) = 840(1.2)
168 + 630X = 1008
630X = 840
X = 840/630 = 280/210 = 4/3
4/3 would be a 33.3333% gain.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
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Jay@ManhattanReview
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Hi emdadul28,emdadul28 wrote:If goods be purchased for 840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
A. 30%
B. 33%
C. 33 1/3%
D. 35%
[ please help me to understand similar maths with a simple and short formula ]
THANKS IN ADVANCE.
Since the question deals with percents, there is no need of the purchase price.
Let us assume that there are four goods, each costing $100. Thus we want an overall profit of 20% on 400 = $80. Or, the combined sale price = 400 + 80 = $480.
We know that one item (one-fourth of four items) is sold for a loss of 20%, or at 100-20=$80.
Thus, we need to get 480 - 80 = $400 from the remaining three items or they be sold at a profit of 400-300=100.
Thus, the profit percentage = (100/300)*100%=33.33%.
The correct answer: C
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Hope this helps!
-Jay
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