How to choose numbers ?

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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

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

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[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]

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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.

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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

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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

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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

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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.

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