If r, s, and w are positive numbers such that x = 60r + 80s

Expert replies

II: Master | Next Rank: 500 Posts; Posts: 400; Joined: Mon Dec 10, 2007 1:35 pm; Location: London, UK; Thanked: 19 times; GMAT Score:680

by II » Sun Jul 13, 2008 2:59 pm

If r, s, and w are positive numbers such that x = 60r + 80s and r + s = 1, is x < 70 ?

(1) r > 0.5

(2) r > s

I got this question correct by plugging-in numbers, but wanted to learn ALTERNATIVE APPROACHES to answer this.
Also what do you think the question is trying to test here ?

My approach:
Start with statement 1 -> let r = 0.6 and s must therefore be 0.4. Plug this back into 60r + 80s = 68. This answers YES to the question "is x < 70?".
Test with r=0.5 and s=0.5, we can see that x=70. So can safely say that if r>0.5 then x<70

Statement 2:
If r > s, then r must be greater than 0.5 (since r + s = 1). We can use the same logic as in statement 1 here. SUFFICIENT.

Answer D.

Thanks in advance.
II

Like this post

Source: Beat The GMAT — Data Sufficiency | Sun Jul 13, 2008 2:59 pm

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Sun Jul 13, 2008 4:01 pm

The equation just represents a weighted average. If r > 0.5, the value will be closer to 60 than to 80.

Think about the equation you'd set up to solve this problem: peanuts cost $60/pound, and cashews cost $80/pound. If a mixture is r% peanuts and s% cashews, what is the cost per pound of the mixture? If you ignore the 100s we need to introduce when dealing with percentages, you should get the same equation as in the question. Clearly if the mixture is more than half peanuts, it will cost less than $70/pound. Each statement tells us that.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Like this post

ramyaravindran: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Mon Apr 28, 2008 5:33 am; Thanked: 2 times

by ramyaravindran » Mon Jul 14, 2008 9:03 am

Not sure if I am incorrect in assuming r to be 0.9 and s to be 0.1. In this case x>72. So, why is the official Answer D. Should it not be E?. Can someone explain?

Like this post

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon Jul 14, 2008 9:15 am

ramyaravindran wrote:Not sure if I am incorrect in assuming r to be 0.9 and s to be 0.1. In this case x>72. So, why is the official Answer D. Should it not be E?. Can someone explain?

You might have made a small arithmetic mistake. If r = 0.9 and s = 0.1, then:

x = 60r + 80s = 60*0.9 + 80*0.1 = 54 + 8 = 62

Like this post

ramyaravindran: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Mon Apr 28, 2008 5:33 am; Thanked: 2 times

by ramyaravindran » Mon Jul 14, 2008 9:28 am

Thanks for the explanation.

Like this post

II: Master | Next Rank: 500 Posts; Posts: 400; Joined: Mon Dec 10, 2007 1:35 pm; Location: London, UK; Thanked: 19 times; GMAT Score:680

by II » Mon Jul 14, 2008 1:10 pm

Also note: one of the most effective ways of solving GMAT inequality problems is to focus on the EXTREME VALUES of a given inequality. This is particularly helpful when solving problems that involve multiple inequalities.

Here we can plug-in extreme values for the r and s inequalities. We know that r must be greater than 0.5 and s must be less than 0.5:
- 60 * (greater than 0.5) = greater than 30
- 80 * (less than 0.5) = less than 40
- So (greater than 30) + (less than 40) = less than 70.

Like this post

rajaram19: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Thu Aug 20, 2009 1:32 pm

WAT IS WRONG HERE?

by rajaram19 » Thu Aug 20, 2009 1:37 pm

w = 60r + 80s ---1
r + s = 1 --2

3--->60r + 60s = 60 adding 1 + 3

w-20s = 60 since there is no 'r' here .Shud E be the answer??wat is the wrong thing i am doin?/plss explain someone

Like this post

adi_800: Legendary Member; Posts: 544; Joined: Thu Oct 08, 2009 9:14 amFollowed by: 2 members; Location: Pune, India; Thanked: 31 times

by adi_800 » Wed Oct 12, 2011 10:17 am

w = 60r + 80s
w = 60r + 60s + 20s
r + s = 1
60r + 60s = 60
Hence, w = 60 + 20s.. Is w < 70 => Is 60 + 2s < 70 => 2s < 10 => Is s < 0.5 ?

Statement 1 -> r > 0.5 => s < 0.5 -> Ans to question is sufficient
Statement 2 -> r > s => Sufficient !!

Like this post

parul9: Master | Next Rank: 500 Posts; Posts: 197; Joined: Thu Sep 15, 2011 10:22 amFollowed by: 2 members; Thanked: 6 times

by parul9 » Wed Oct 12, 2011 10:25 am

It is D!
I followed adi_800's method!

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: If r, s, and w are positive numbers such that x = 60r + 80s

by Brent@GMATPrepNow » Mon Feb 07, 2022 7:40 am

II wrote: ↑
Sun Jul 13, 2008 2:59 pm
If r, s, and w are positive numbers such that x = 60r + 80s and r + s = 1, is x < 70 ?

(1) r > 0.5
(2) r > s

Given: r, s, and w are positive numbers such that w = 60r + 80s and r + s = 1

Target question: w < 70
STRATEGY: Always be on the lookout for opportunities to rephrase the target question. In many cases, a little work up front will make analyzing the statements much easier.

Since we're told that r + s = 1, we might recognize that we can manipulate the equation w = 60r + 80s to take advantage of this information.
We can write: w = (60r + 60s) + 20s
Then factor the first part to get: w = 60(r + s) + 20s
Substitute to get: w = 60(1) + 20s
In other words: w = 60 + 20s, which means the target question becomes: Is 60 + 20s < 70?
We can make things even easier by subtracting 60 from both sides to get: Is 20s < 10?
And we can divide both sides by 20 to get: Is s < 0.5?
REPHRASED target question Is s < 0.5?

Aside: Here’s a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: r > 0.5
We already know that r + s = 1
So, for example, if r = 0.5, then s = 0.5
Similarly, if r > 0.5, we can be certain that s < 0.5
In other words, the answer to the REPHRASED target question is YES, s is less than 0.5
Statement 1 is SUFFICIENT

Statement 2: r > s
If r + s = 1, we can subtract s from both sides to get: r = 1 - s
Now take statement 2 and replace r with 1 - s to get: 1 - s > s
From here, we can add s do both sides of the inequality to get: 1 > 2s
Divide both sides by 2 to get: 0.5 > s
Once again, the answer to the REPHRASED target question is YES, s is less than 0.5
Statement 2 is SUFFICIENT

Answer: D

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review