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ved · 2007 August 2nd, 10:46 PM

A certain car dealership sells only full-size and mid-size cars. One of its sales representatives
receives an annual salary of $15,000. He also receives a commission of $800 for each full-size
car he sells and $500 for each midsize car he sells. What is the least number of cars he must
sell in a year to receive total annual earnings of exactly $25,000?
(A) 7
(B) 12
(C) 13
(D) 14
(E) 17

OA : 14

I used this approach to solve the problem
8x + 5y = 100
And then did a couple of combinations before i could arrive at the answer.But given the stringent time pressure this would be a bad approach.
Is there a better approach to this?

GRE_Kickboxer · 2007 August 3rd, 01:10 AM

I'm curious to know what you think of my method? I prefer this type of reasoning over pure algebra a lot of the time (although not always). Please feel free to tell me if you think my method isn't straightforward enough. I want to know how others approach problems.

Look at the equation that you yourself wrote:

8x + 5y = 100

Inductive reasoning steps:

First, we really need to deeply understand how factors and multiples of different numbers affect one another.

What is the equation telling us? It is telling us that we have find the greatest multiple of 8 that is less than 100 and that is also a multiple of 5.

After all, we want to get to 100 with the least amount of x units + y units.

Therefore 8 x 10, and 5 x 4 equals the total of 100.

10 + 4 = 14

Do you like this method, or would this not work for you? In the end, logic is your biggest weapon for any section of the GRE.

benchy · 2007 August 3rd, 04:03 AM

Can I ask Mr.GRE_Kickboxer? from your methods

8x + 5y = 100

u said that we have find the greatest multiple of 8 that is less than 100 and that is also a multiple of 5.
But if I just realized some numbers as below

8(5) + 5(12) = 100

The answer will be 12 + 5 = 17 ???

Could you pls explain why we should find the greatest multiple of 8 befor we find the multiple of 5??

GRE_Kickboxer · 2007 August 3rd, 06:05 AM

Hi Benchy. You have to remember that the goal is to sell the least number of cars possible. The way you solved the problem results in 3 extra required sales.

It would be ideal if we could only sell the higher priced cars. The problem is that we can't multiply 8 by any integers and get 100. We have to sell 4 lower priced cars otherwise we won't land on 100 when we add things up.

The least number of sales that need to be made given the formula 8x + 5y = 100
is 14.

benchy · 2007 August 3rd, 07:25 AM

Thanks GRE_Kickboxer, you reminded me that I should read the questions very carefully

ved · 2007 August 3rd, 01:28 PM

Thanks Gre_kickboxer and Benchy,

GRE_Kickboxer your post definitely provides useful improvisation over my line of thinking.
eg.
What is the equation telling us? It is telling us that we have find the greatest multiple of 8 that is less than 100 and that is also a multiple of 5.

Have to start thinking as clearly as this.I hate to plug in numbers

Although what I was looking for a different line of logic. Nonetheless I presume this will save my time as well

GRE_Kickboxer · 2007 August 3rd, 02:57 PM

ved: I'm positive you can think that clearly. It's just about insight. Insight into math problems is kind of cool because a lot of the time it improves suddenly. You practice problems for awhile, feel like you aren't getting much better, and then suddenly your ability to do them improves. Instead of improving linearly, it SOMETIMES improves suddenly.

The way to develop insight is by understanding what the fundamentals truly mean in a way that makes sense to you. Why do we use equations and set things equal to each other? When is doing that appropriate? What is the purpose of prime numbers and what do they really mean? How do numbers relate to each other on a number line? What happens to different types of numbers when you divide by decimals, multiply by decimals, square decimals etc. When you study problems with this type of mentality, and pay attention to what happens, you develop the ability to be insightful, faster. A lot of it has to do with paying attention to what is happening when you solve problems and then using good common sense and logic.

learner85 · 2007 September 1st, 08:20 PM

can any1 solve the problem in step-by-step to show how it works??????????

chowdhury

zulkfal · 2007 September 5th, 03:00 AM

Quote:

Originally Posted by learner85

can any1 solve the problem in step-by-step to show how it works??????????

chowdhury

As perr question we set up the following equation

15000+800X+500Y=25000

Subtracting 15000 from both sisdes yields

800X+500Y=10000

dividing both sides by 100 to reduce the equation on lowest level (Quicker to solve)

we got

8X+5Y=100

Now as said in above replies least GCM of 8 which is less than 100 and also multiple of 5

so we got 4 and 10

now subtitute

8(10) + 5(4) = > 80 + 20 = 100

2007 August 2nd, 10:46 PM	#1 (permalink)
ved Eager! Join Date: Jun 2007 Posts: 73	GRE Math : Need a Better Approach A certain car dealership sells only full-size and mid-size cars. One of its sales representatives receives an annual salary of $15,000. He also receives a commission of $800 for each full-size car he sells and $500 for each midsize car he sells. What is the least number of cars he must sell in a year to receive total annual earnings of exactly $25,000? (A) 7 (B) 12 (C) 13 (D) 14 (E) 17 OA : 14 I used this approach to solve the problem 8x + 5y = 100 And then did a couple of combinations before i could arrive at the answer.But given the stringent time pressure this would be a bad approach. Is there a better approach to this? _ _ _ _ SIG _ _ _ _ Knowing is better than wondering Last edited by ved : 2007 August 2nd at 10:48 PM. Reason: changed the text

2007 August 3rd, 01:28 PM	#6 (permalink)
ved Eager! Join Date: Jun 2007 Posts: 73	Thanks Gre_kickboxer and Benchy, GRE_Kickboxer your post definitely provides useful improvisation over my line of thinking. eg. What is the equation telling us? It is telling us that we have find the greatest multiple of 8 that is less than 100 and that is also a multiple of 5. Have to start thinking as clearly as this.I hate to plug in numbers Although what I was looking for a different line of logic. Nonetheless I presume this will save my time as well _ _ _ _ SIG _ _ _ _ Knowing is better than wondering

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2007 August 3rd, 01:10 AM	#2 (permalink)
GRE_Kickboxer Within my grasp! Join Date: Jun 2007 Posts: 469	I'm curious to know what you think of my method? I prefer this type of reasoning over pure algebra a lot of the time (although not always). Please feel free to tell me if you think my method isn't straightforward enough. I want to know how others approach problems. Look at the equation that you yourself wrote: 8x + 5y = 100 Inductive reasoning steps: First, we really need to deeply understand how factors and multiples of different numbers affect one another. What is the equation telling us? It is telling us that we have find the greatest multiple of 8 that is less than 100 and that is also a multiple of 5. After all, we want to get to 100 with the least amount of x units + y units. Therefore 8 x 10, and 5 x 4 equals the total of 100. 10 + 4 = 14 Do you like this method, or would this not work for you? In the end, logic is your biggest weapon for any section of the GRE.

2007 August 3rd, 04:03 AM	#3 (permalink)
benchy Eager! Join Date: Mar 2007 Posts: 70	Can I ask Mr.GRE_Kickboxer? from your methods 8x + 5y = 100 u said that we have find the greatest multiple of 8 that is less than 100 and that is also a multiple of 5. But if I just realized some numbers as below 8(5) + 5(12) = 100 The answer will be 12 + 5 = 17 ??? Could you pls explain why we should find the greatest multiple of 8 befor we find the multiple of 5??

2007 August 3rd, 06:05 AM	#4 (permalink)
GRE_Kickboxer Within my grasp! Join Date: Jun 2007 Posts: 469	Hi Benchy. You have to remember that the goal is to sell the least number of cars possible. The way you solved the problem results in 3 extra required sales. It would be ideal if we could only sell the higher priced cars. The problem is that we can't multiply 8 by any integers and get 100. We have to sell 4 lower priced cars otherwise we won't land on 100 when we add things up. The least number of sales that need to be made given the formula 8x + 5y = 100 is 14.

2007 August 3rd, 07:25 AM	#5 (permalink)
benchy Eager! Join Date: Mar 2007 Posts: 70	Thanks GRE_Kickboxer, you reminded me that I should read the questions very carefully

2007 August 3rd, 02:57 PM	#7 (permalink)
GRE_Kickboxer Within my grasp! Join Date: Jun 2007 Posts: 469	ved: I'm positive you can think that clearly. It's just about insight. Insight into math problems is kind of cool because a lot of the time it improves suddenly. You practice problems for awhile, feel like you aren't getting much better, and then suddenly your ability to do them improves. Instead of improving linearly, it SOMETIMES improves suddenly. The way to develop insight is by understanding what the fundamentals truly mean in a way that makes sense to you. Why do we use equations and set things equal to each other? When is doing that appropriate? What is the purpose of prime numbers and what do they really mean? How do numbers relate to each other on a number line? What happens to different types of numbers when you divide by decimals, multiply by decimals, square decimals etc. When you study problems with this type of mentality, and pay attention to what happens, you develop the ability to be insightful, faster. A lot of it has to do with paying attention to what is happening when you solve problems and then using good common sense and logic.

2007 September 1st, 08:20 PM	#8 (permalink)
learner85 Eager! Join Date: Sep 2007 Posts: 46	can any1 solve the problem in step-by-step to show how it works?????????? chowdhury

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