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# A small textile company buys few machines to stitch garments, costing

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Math Expert
Joined: 02 Sep 2009
Posts: 56304
A small textile company buys few machines to stitch garments, costing  [#permalink]

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24 Sep 2018, 05:44
00:00

Difficulty:

15% (low)

Question Stats:

88% (01:18) correct 12% (01:24) wrong based on 33 sessions

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A small textile company buys few machines to stitch garments, costing a total of \$10,000. The per unit cost of each garment is \$2.50 and is sold for \$4.50. How many units of the garments must be sold to achieve break-even (A phenomenon when all the investment and production costs are recovered by the sales revenue)?

(A) 2000
(B) 3500
(C) 4500
(D) 5000
(E) 6000

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A small textile company buys few machines to stitch garments, costing  [#permalink]

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Updated on: 24 Sep 2018, 21:39
Bunuel wrote:
A small textile company buys few machines to stitch garments, costing a total of \$10,000. The per unit cost of each garment is \$2.50 and is sold for \$4.50. How many units of the garments must be sold to achieve break-even (A phenomenon when all the investment and production costs are recovered by the sales revenue)?

(A) 2000
(B) 3500
(C) 4500
(D) 5000
(E) 6000

Let, Number of sold units = x

For Break-Even, COST = REVENUE

i.e. 10,000+2.5*x = 4.5*x

i.e. 2x = 10000

i.e. x = 5000

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Originally posted by GMATinsight on 24 Sep 2018, 20:06.
Last edited by GMATinsight on 24 Sep 2018, 21:39, edited 1 time in total.
Math Expert
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Posts: 56304
Re: A small textile company buys few machines to stitch garments, costing  [#permalink]

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24 Sep 2018, 20:58
GMATinsight wrote:
Bunuel wrote:
A small textile company buys few machines to stitch garments, costing a total of \$10,000. The per unit cost of each garment is \$2.50 and is sold for \$4.50. How many units of the garments must be sold to achieve break-even (A phenomenon when all the investment and production costs are recovered by the sales revenue)?

(A) 2000
(B) 3500
(C) 4500
(D) 5000
(E) 6000

Total Cost = 10000
Per unit cost = 2.5
Total units = 10,000/2.5 = 4000

Let, Number of sold units = x

For Break-Even, COST = REVENUE

i.e. 10,000 = 4.5*x

i.e. x = 2223

Bunuel The answer choices are incorrect

The question implies that (the total cost to produce n units) = (cost of machines) + (per unit cost) = \$10,000 + \$2.5*x.
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Re: A small textile company buys few machines to stitch garments, costing  [#permalink]

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24 Sep 2018, 21:27
I went with the back solving method here.

2.50 x 5000 = 12,500 +10,000 = 22,500
4.50 x 5000 = 22,500

Answer is D but I took around 2 mins and 30 seconds to find the answer. Can someone show me a better approach please?

Thank you
Arjun
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Re: A small textile company buys few machines to stitch garments, costing  [#permalink]

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24 Sep 2018, 21:39
ArjunJag1328 wrote:
I went with the back solving method here.

2.50 x 5000 = 12,500 +10,000 = 22,500
4.50 x 5000 = 22,500

Answer is D but I took around 2 mins and 30 seconds to find the answer. Can someone show me a better approach please?

Thank you
Arjun

Check the solution above...
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Re: A small textile company buys few machines to stitch garments, costing  [#permalink]

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25 Sep 2018, 00:19
since 4.5>2.5
then profits will cover 10,000
so 10,000/2 = 5000 means at 5000 the initial cost + 10,000 will be covered
is this approach correct?
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Re: A small textile company buys few machines to stitch garments, costing  [#permalink]

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25 Sep 2018, 03:28
manjot123 wrote:
since 4.5>2.5
then profits will cover 10,000
so 10,000/2 = 5000 means at 5000 the initial cost + 10,000 will be covered
is this approach correct?

manjot123

Absolutely Correct...
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Re: A small textile company buys few machines to stitch garments, costing   [#permalink] 25 Sep 2018, 03:28
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