Abominable AB

[dverma4830]

If a and b are integers, and |a| > |b|, is a · |b| < a - b?

(1) a < 0

(2) ab >= 0


The solution given is too cumbersome.....I don't think I can ever do so much work in less than3-4 mins

[messi10]

Hi,

Tough one..

We have the absolute value of a is greater than the absolute value of b. This means that positive or negative, the numerical value of a is always greater than the numerical value of b.

Statement 1: a < 0
i.e. a is negative
Therefore, a·|b| = negative x positive = negative

We don't know anything about b so we will have to take all three cases in which b is positive or negative or zero. We only know from the question that the numerical value of a is greater than that of b. Lets pick numbers quickly:

Code: Select All Code

  a     b       a·|b|          a-b             Is a·|b| < a-b ?
-10     0         0            -10                    No
-10    -5        -50            -5                   Yes
-10    +5        -50           -15                   Yes

Therefore statement 1 is insufficient

Statement 2: ab >= 0

We have three situations:
i) a and b are both positive
ii) a and b are both negative
iii) b = 0

Note that "a" cannot be equal to zero because then the absolute value can never be greater than b.

Again, lets make a quick table:

Code: Select All Code

a       b        a·|b|           a-b          Is a·|b| < a-b ?
10      5         50              5                   No
-10    -5         50             -5                   No
10      0          0              10                  Yes
-10     0          0             -10                  No


Therefore statement 2 is also insufficient.

Combining 1 and 2, we know that a <0 and ab>=0. This means that b is either negative or zero

Quick table once more:

Code: Select All Code

a     b        a·|b|          a-b           Is a·|b| < a-b ?
-10   -5         50           -5                   No
-10    0         0           -10                   No


Therefore, statements 1 and 2 together are sufficient and answer is C

Please post the OA

Thanks

Sunil

[dverma4830]

OA is E

[messi10]

haha! Took me almost 20 mins to type that solution. So much for that... :)

Can you please post a summary of the answer or point out where I went wrong?

Thanks

Sunil

[messi10]

ah, I found my mistake. Its in the last table, first line.
When a = -10 and b = -5
a·|b| = -50

I have put 50 instead.

So that changes the table to the following:

Code: Select All Code

a     b        a·|b|          a-b           Is a·|b| < a-b ?
-10   -5        -50           -5                   Yes
-10    0         0           -10                   No


And so the answer is E.

In your post, you seem a little worried about the solution being too cumbersome. It does seem like that initially, but bear in mind that at the end of the day, all we are doing is picking the right combination of numbers. If you are comfortable with the concept of absolute values then this should not be hard. Its just tedious. A bit cruel as well... one small mistake and all that work is almost useless. :)

One more thing that works for me. If I don't have a clue about a question, I look at the solution. Sometimes I have the same reaction as you did - "This is way over my level". I leave it, come back to it after a week and try to do the question on my own. One of two things happen:
1) I get stuck again but this time I went further than the last.
OR
2) I get it right and feel more confident about the topic.

If (1) happened, I come back to it again after a week, maybe longer. Chances are that I will get it right this time.

Try it, I am sure it will work for you too

Regards

Sunil

[dverma4830]

Thanks a lot!!!!
As you have suggested I have decided to leave this alone for sometime will come back to it in a day or two.....
I m sure will do better on this then
Cheers
Dheeraj

[jnelson0612]

Excellent!

As Sunil demonstrated, number testing can be the best strategy for DS questions involving variables.