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OG-2nd Edition - Question 114 & 134

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OG-2nd Edition - Question 114 & 134

by shanice » Sun Aug 05, 2012 8:11 pm
1)Salesperson A's compensation for any week is $360 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation?

(A)$21,000
(B)$18,000
(C)$15,000
(D)$4,500
(E)$4,000

Answer is C.

2)If d>0 and 0<1-c/d<1, which of the following must be true?

I . c>0
II . c/d<1
III. c^2+d^2>1

(A)I only
(B)II only
(C)I and II only
(D)II and III only
(E)I,II and III


Answer is C.

Please help me with step by step explanation.

Thank you.
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by Anurag@Gurome » Sun Aug 05, 2012 8:24 pm
shanice wrote:1)Salesperson A's compensation for any week is $360 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation?

(A)$21,000
(B)$18,000
(C)$15,000
(D)$4,500
(E)$4,000

Answer is C.

Please help me with step by step explanation.

Thank you.
Let the total weekly sales = $S (here both salespersons A and B earn the same amount)
Then 360 + 6% of (S - 1000) = 8% of S
360 + 0.06(S - 1000) = 0.08S
360 + 0.06S - 60 = 0.08S
0.02S = 300
S = [spoiler]$15,000[/spoiler]

The correct answer is C.
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by Anurag@Gurome » Sun Aug 05, 2012 8:30 pm
shanice wrote: 2)If d>0 and 0<1-c/d<1, which of the following must be true?

I . c>0
II . c/d<1
III. c^2+d^2>1

(A)I only
(B)II only
(C)I and II only
(D)II and III only
(E)I,II and III

Answer is C.

Please help me with step by step explanation.

Thank you.
0 < 1 - c/d < 1 implies c/d < 1
Since d > 0, so c > 0 so that c < d
Hence, we know that I and II are true.

We know that c < d
If c = 1, d = 2, then c² + d² = 1² + 2² = 1 + 4 = 5, which is > 1. Here c < d.
If c = 2, d = 1, then c² + d² = 2² + 1² = 4 + 1 = 5, which is > 1. Here c > d.
So, III may or may not be true.

The correct answer is C.
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by GMATGuruNY » Mon Aug 06, 2012 3:28 am
shanice wrote:1)Salesperson A's compensation for any week is $360 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of B's total sales for that week. For what amount of total weekly sales would both salespeople earn the same compensation?

(A)$21,000
(B)$18,000
(C)$15,000
(D)$4,500
(E)$4,000
We can plug in the answers, which represent the total sales.
When the correct answer is plugged in, A's compensation = B's compensation.
We should start with C, the middle answer choice.

C: 15,000
Here, A's sales above 1000 = 15000-1000 = 14000.
A's compensation = 360 + .06(14000) = 360 + 840 = 1200.
B's compensation = .08(15000) = 1200.
Success!

The correct answer is C.
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by GMATGuruNY » Mon Aug 06, 2012 3:40 am
shanice wrote: If d>0 and 0<1-c/d<1, which of the following must be true?

I . c>0
II . c/d<1
III. c^2+d^2>1

(A)I only
(B)II only
(C)I and II only
(D)II and III only
(E)I,II and III
To satisfy the condition that 0 < 1- c/d < 1, c/d must be a positive fraction between 0 and 1.
Thus, II must be true.
Eliminate A.

Since d>0, in order for c/d to be a positive fraction between 0 and 1, c>0.
Thus, I must be true.
Eliminate B and D.

When a problem is not restricted to integers, BE SURE TO CONSIDER FRACTIONS.

If c = 1/4 and d = 3/4, then c/d = (1/4)/(3/4) = 1/3, satisfying the requirement that c/d be a positive fraction between 0 and 1.
If we plug c = 1/4 and d = 3/4 into III, we get:
c² + d² = (1/4)² + (3/4)² = 1/16 + 9/16 = 10/16 = 5/8, which is not greater than 1.
Thus, III does not have to be true.
Eliminate E.

The correct answer is C.
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by shanice » Fri Aug 10, 2012 12:38 am
Hi Mr.Anurag,

Let the total weekly sales = $S (here both salespersons A and B earn the same amount)
Then 360 + 6% of (S - 1000) = 8% of S
360 + 0.06(S - 1000) = 0.08S
360 + 0.06S - 60 = 0.08S
0.02S = 300
S = $15,000

The correct answer is C

As per your workings, why can't 360 + 6% of (S + 1000) = 8% of S ?

Thank you in advance.
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by aguirrestom » Sun Jun 07, 2015 10:53 am
Image

114)
Salesperson A's compensation for any week is $360 plus..

Adding a visual graph to answer any questions out there--hope this helps!
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