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Difficulty:   65% (hard)

Question Stats: 58% (02:52) correct 42% (03:03) wrong based on 31 sessions

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Erica receives an annual salary of $38,000 plus a commission of 20 percent on sales she makes in excess of$90,000 while Carla receives an annual salary of $24,000 plus a 10 percent commission on her total annual sales only if they exceed$150,000. If Erica earned twice as much as Carla, and both realized equal sales for their company, what must the total annual sales made by each?

A. $95,000 B.$120,000
C. $140,000 D.$160,000
E. $180,000 _________________ Senior SC Moderator V Joined: 22 May 2016 Posts: 3581 Erica receives an annual salary of$38,000 plus a commission of 20 per  [#permalink]

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Bunuel wrote:
Erica receives an annual salary of $38,000 plus a commission of 20 percent on sales she makes in excess of$90,000 while Carla receives an annual salary of $24,000 plus a 10 percent commission on her total annual sales only if they exceed$150,000. If Erica earned twice as much as Carla, and both realized equal sales for their company, what must the total annual sales made by each?

A. $95,000 B.$120,000
C. $140,000 D.$160,000
E. $180,000 Use answer choices Algebra is probably slower for most. Quant is not a test of how well you do algebra. Using answer choices frequently saves time. Start with Answer C to get a benchmark. C)$140,000. If both sold $140,000 Erica - Erica gets a 20% commission only on sales over$90,000

Amount of sales greater than $90,000: (140,000 - 90,000) =$50,000

Erica's 20% commission on $50,000: (.2*$50,000)= $10,000 Erica's total earnings: Base + Commission$38,000 + $10,000 =$48,000

Carla
Gets no commission. (She gets commission only on sales greater than $150,000, and (C) is 140,000.) Carla's total earnings: Base =$24,000

Erica earned twice as much as Carla?
$48,000 = 2($24,000) Correct

Algebra
IMO, unless you really prefer algebra, avoid it.

Erica's earnings:
$38,000 + .20(x -$90,000)
$38,000 + .20x -$18,000
$20,000 + .20x Carla's earnings:$24,000 + .10(x - $150,000)$24,000 + .10x - $15,000$9,000 + .10x

Erica earns twice as much as Carla, so
E = 2C
$20,000 + .20x = 2($9,000 + .10x)
$20,000 + .20x =$18,000 + .20x
$20,000 =$18,000
False. No solution. The variables canceled each other.

There is only one possibility: commissions for Carla cannot figure in, which means that she did not make more than $150,000 in sales. (Commissions for Erica figure in. Answer choices are all >$90,000.)

So Erica, earning (Base + Commission), earns twice as much as Carla, who earns Base only.
E = 2C
38,000 + .20(x-90,000) = (2)* 24,000
38,000 + .20x - 18,000 = 48,000
20,000 + .2x = 48,000
.2x = 28,000
x = 28,000/.20
x = $140,000 Answer C _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. If you ask for kudos, you had better be ready to give them. Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver Director  P Joined: 24 Nov 2016 Posts: 641 Location: United States Erica receives an annual salary of$38,000 plus a commission of 20 per  [#permalink]

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Bunuel wrote:
Erica receives an annual salary of $38,000 plus a commission of 20 percent on sales she makes in excess of$90,000 while Carla receives an annual salary of $24,000 plus a 10 percent commission on her total annual sales only if they exceed$150,000. If Erica earned twice as much as Carla, and both realized equal sales for their company, what must the total annual sales made by each?

A. $95,000 B.$120,000
C. $140,000 D.$160,000
E. $180,000 $$e=38k+0.2(x-90k);c=24k…=24k+0.1x;e=2c$$ $$sales > 150k;38k+0.2(x-90k)=2(24k+0.1x)… 38k+0.2x-18k=48k+0.2x…-28k=0…invalid$$ $$sales < 150k; 38k+0.2(x-90k)=2(24k)…38k+0.2x-18k=48k…28k=0.2x…x=28k/0.2=140k$$ Answer (C) Erica receives an annual salary of$38,000 plus a commission of 20 per   [#permalink] 08 Sep 2019, 04:51
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