Is a-d less than b-c?

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Comment on Is a-d less than b-c?

I was wondering that can we

nehashekhawat - January 15, 2017

I was wondering that can we also apply adding rule of inequalities in the second statement and prove that it is sufficient as second statement forms 2 inequalities i.e a<b and c<d so by applying adding rule we can write it as a+c<b+d,which makes the given statement sufficient

That's a great approach - it

gmat-admin - January 16, 2017

That's a great approach - it uses a technique covered in this video: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

Because this question appears early in the video course (in the Arithmetic module), we solved it using some number sense, rather than apply techniques we haven't covered yet.

Great work!

Is using these big and small

internetgeek - June 11, 2017

Is using these big and small +/- sign a shortcut and can one assume it will almost (if not always) work for these types of questions?

The technique will help with

gmat-admin - June 12, 2017

The technique will help with some questions, but not with others. Just add it to the other "tools" in your math strategies toolbox, and sometimes it will come in handy.

Dear Brent,

userefca3c - September 1, 2018

Dear Brent,

From where can i get og 2019? I don't have that.

Here's one place: https:/

gmat-admin - September 1, 2018

Here's one place: https://gmatclub.com/forum/gmac-official-guides-the-master-directory-lin...

Cheers,
Brent

We can also rearrange the

ari.banerjee - January 8, 2019

We can also rearrange the question stem as Is a-b<d-c?

Since option 2 says that both a and b are negative and c and d are positive, and d is greater than c, (d-c) will be a positive value. Hence, this satisfies the question stem.

Is this approach right?

Thank you!

That's a great way to

gmat-admin - January 8, 2019

That's a great way to rephrase the target question!

REPHRASED target question: Is a - b < d - c?

If a < b, then a - b must be NEGATIVE
And, if c < d, then d - c must be POSITIVE

So, the answer to the REPHRASED target question is a definite "Yes!"

Great work.

Cheers,
Brent

I manipulated the equation a

sterlingarcher123 - February 5, 2019

I manipulated the equation a-d < b-c to try and simplify the question as per your suggestions in other videos:

Here's what i got.

a - d < b - c
a + c < b + d
multiply both sides by -1 and change signs
-a - c > -b - d
-a + d > -b + c

Is this appropriate in answering Statement 1?

I believe you are REPHRASING

gmat-admin - February 5, 2019

I believe you are REPHRASING the target question as "Is -a + d > -b + c?"

Statement 1) a + d < b + c

Offhand, it's hard to tell whether your rephrased target question will help us analyze whether statement 1 is sufficient, because the elements of your rephrased target question are still different from the elements of the target question.

So, we're stuck with either manipulating the inequalities (to try to make them look more similar) or testing values.

Let's test some values.

CASE A: a = 0, b = 2. c = 3, d = 0. In this case, the answer to the REPHRASED target question is "NO, -a + d is NOT greater than -b + c"

CASE B: a = 0, b = 5. c = 1, d = 0. In this case, the answer to the REPHRASED target question is "YES, -a + d IS greater than -b + c"

Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Does that help?

Cheers,
Brent

In evaluating Statement 2, I

cabilesv2020 - December 26, 2019

In evaluating Statement 2, I simply assigned these values:
a = -2
b = -1
c = 1
d = 2
So, (a-d) < (b-c) => -4 < -2 => Yes, sufficient.
Is this okay? Thanks.

Be careful. Testing values

gmat-admin - December 26, 2019

Be careful. Testing values will never yield a definitive result unless you get contradictory answers to the target question.

Consider this rudimentary question:

Is xy positive?
(1) x + y > 0

Let's test a pair of values that satisfy statement 1.
Since x + y > 0, it COULD be the case x = 1 and y = 2
In this case, xy = (1)(2) = 2
So the answer to the target question is "YES, xy is positive"
Does this mean that statement 1 is sufficient?
No. Since we have tested only one pair of values, we cannot be certain that xy will ALWAYS be positive.

In fact, if we test x = -1 and y = 2, we will find that, this time, the answer to the target question is "NO, xy is not positive"

As I mentioned above, testing values will never yield a definitive result unless you get contradictory answers to the target question.

For more on this, start watching the following video at 5:55 : https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1101

Cheers,
Brent

Hi Brent, wondering why is

Kimberly750 - October 23, 2022

Hi Brent, wondering why is testing values are ok with St1 but not with St2? Any particular reason in this case here? Thanks

Testing values is a great way

gmat-admin - October 23, 2022

Testing values is a great way to show that a statement is not sufficient because this strategy can show scenarios that yield different answers to the target question.
However, if the statement is sufficient, then testing values won't yield any conclusive results.

So, if it SEEMS (feels) like a statement does not provide sufficient information, then testing values can be useful.
However, if a statement doesn't seem sufficient, then testing values is of limited value.

Here's an article I wrote about this: https://www.gmatprepnow.com/articles/data-sufficiency-when-plug-values

Make perfect sense. Thanks

Kimberly750 - October 23, 2022

Make perfect sense. Thanks Brent and very much appreciated for your great helps always!!

Hi Brent,

V Hari krishna - July 26, 2020

Hi Brent,

I rephrased the question: b-c > a-d?
a-d < b-c?

statement-1: a+d < b+c; taking minus "-" as common from both sides, it evaluates to a-d > b-c. Hence it does not satisfy any of the target questions. so insufficient.

statement-2: a<b<0<c<d; I have taken values here as per the given statement.

a=-2,b=-1,c=1,d=2; then a-d=-2-2=-4;
b-c=-1-1=-2;
Hence a-d is less than b-c and it satisfies the target question. So sufficient.

Ans:B

Be careful with that approach

gmat-admin - July 27, 2020

Be careful with that approach. Testing only ONE set of values does not yield definitive results. It could have been the case that testing a different set of values would have yielded a different answer.

This is one of the limitations of testing values: If testing values does not lead to different answers to the target question, we can never be certain of the correct answer. I covered this limitation in the following video (starting at 8:30): https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1101

Hi Brent,

Adityavikram12 - September 11, 2021

Hi Brent,
Can we also rephrase the main question in the following manner?
Main Question => a-d < b-c
Rephrased => a-b < d-c

Stt 1- a+d < b+c OR a-b < c-d
Now that we have a-b on the left in both the case, all we have to check is if d-c or c-d is greater than a-b
(using a couple of numbers proves that it is insufficient)

and we move on the 2nd statement and so on..

Is my approach for the first statement correct?

Thanks

That's a perfect approach.

gmat-admin - September 11, 2021

That's a perfect approach. Nice work!

Question: Is a-d less than b-c?

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Comment on Is a-d less than b-c?

I was wondering that can we

That's a great approach - it

Is using these big and small

The technique will help with

Dear Brent,

Here's one place: https:/

We can also rearrange the

That's a great way to

I manipulated the equation a

I believe you are REPHRASING

In evaluating Statement 2, I

Be careful. Testing values

Hi Brent, wondering why is

Testing values is a great way

Make perfect sense. Thanks

Hi Brent,

Be careful with that approach

Hi Brent,

That's a perfect approach.

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