How to choose numbers ?

Expert replies

Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Tue Oct 01, 2013 6:49 pm

If a,b,c,d are positive number, is a/b less than c/d ?

1) 0 less than (c-a)/(d-b)
2) ((ad)/(bc))^2 less than (ad)/(bc)

I got trapped by first statement,
it says a+d less than c+b, so I came to conclusion that (c*b) must be grater than (a*d).....

But I am wrong..
The number I choose made me to come to conclusion.I failed to choose the value of
a =4,b=6,c=2,d=3.

So, Please help me how should I choose numbers, not only for this question, for all types of question. If any where some one wrote about choosing numbers topic pls share with me.

Thanks in advance:)

Source OG13: Q:92

For others who want to try
OA is B

Like this post

Source: Beat The GMAT — Data Sufficiency | Tue Oct 01, 2013 6:49 pm

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Oct 01, 2013 6:57 pm

Hi Uva@90,

Here's a video explanation that you'll find helpful:

Watch Rich CRUSH this DS question...

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Oct 02, 2013 2:43 am

If a, b, c, and d, are positive numbers, is a/b < c/d?

(1) 0 < (c-a) / (d-b)

(2) (ad/bc)^2 < (ad)/(bc)

Statement 1: (c-a) / (d-b) > 0
Make c and d both greater than a and b.
Try two cases:
c > d, so that c/d > 1.
c < d, so that c/d < 1.

Case 1: a=1, b=1, c=3, and d=2.
In this case, a/b = 1 and c/d = 3/2, so a/b < c/d.

Case 2: a=1, b=1, c=2, and d=3.
In this case, a/b = 1 and c/d = 2/3, so a/b > c/d.
INSUFFICIENT.

Statement 2: (ad/bc)Â² < (ad)/(bc)
Since all of the values are positive, we can rephrase the question stem by cross-multiplying:
a/b < c/d
ad < bc.
Question stem rephrased: Is ad < bc?

Since all of the values are positive, we can divide each side of statement 2 -- (ad/bc)Â² < (ad)/(bc) -- by ad/bc, yielding the following:
ad/bc < 1
ad < bc.
SUFFICIENT.

The correct answer is B.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

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

by Brent@GMATPrepNow » Wed Oct 02, 2013 6:40 am

If you're interested, we have a free video called Choosing Good Numbers : https://www.gmatprepnow.com/module/gmat- ... cy?id=1102

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Thu Oct 03, 2013 6:01 am

Rich/Mitch/Brent,

Thanks all for your valuable help

Like this post

GMAT/MBA Expert

ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Fri Oct 04, 2013 12:50 pm

This problem can be solved without choosing numbers, if you rephrase the question:

is a/b less than c/d ?
Because all of these variables are positive, we're allowed to cross-multiply here:
a/b < c/d
ad < bc?

Often it's easier to deal with products than with ratios on DS questions.

Statement 1: 0 < (c-a)/(d-b)
Here, we can't cross-multiply, because we don't know if (d - b) is positive or negative. Our question was asking us about ratios/products... in other words, PROPORTIONAL relationships. This statement is giving us information about DIFFERENCES, which cannot answer a proportion question. (You can certainly test numbers to prove the point, though, as Mitch pointed out).
Insufficient

Statement 2: (ad/bc)Â² < (ad)/(bc)
Here, we're given a proportion, which is already more helpful. Let's rephrase:
(ad/bc)Â² < (ad)/(bc) Because everything is positive, we know that all products and ratios will be positive. If the square of the ratio (ad/bc) is less than the ratio itself, what does that mean? It means the ratio must be a POSITIVE FRACTION.
ad/bc < 1
Multiply both sides by bc:
ad < bc
This is our target question. Sufficient.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

Like this post

Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Fri Oct 04, 2013 6:35 pm

ceilidh.erickson wrote:This problem can be solved without choosing numbers, if you rephrase the question:

is a/b less than c/d ?
Because all of these variables are positive, we're allowed to cross-multiply here:
a/b < c/d
ad < bc?

Often it's easier to deal with products than with ratios on DS questions.

Statement 1: 0 < (c-a)/(d-b)
Here, we can't cross-multiply, because we don't know if (d - b) is positive or negative. Our question was asking us about ratios/products... in other words, PROPORTIONAL relationships. This statement is giving us information about DIFFERENCES, which cannot answer a proportion question. (You can certainly test numbers to prove the point, though, as Mitch pointed out).
Insufficient

Statement 2: (ad/bc)Â² < (ad)/(bc)
Here, we're given a proportion, which is already more helpful. Let's rephrase:
(ad/bc)Â² < (ad)/(bc) Because everything is positive, we know that all products and ratios will be positive. If the square of the ratio (ad/bc) is less than the ratio itself, what does that mean? It means the ratio must be a POSITIVE FRACTION.
ad/bc < 1
Multiply both sides by bc:
ad < bc
This is our target question. Sufficient.

Ceilidh Erickson,
Thats's a cool strategy you have pointed out.
Question ask about the ratios but statement provides their difference. Hence it proved that statement 1 is INSUFFICIENT.

I thank you for providing this idea.

Regards,
Uva.

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