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Please Help !!! tough question

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Please Help !!! tough question

by evs.teja » Tue Dec 23, 2014 5:34 pm
Hii, this is a MGMAT mock question. Please don't forget to explain your approach

If ab ≠ 0 and a + b ≠ 0, is 1/(a+b)< 1/a + 1/b ?

(1) |a| + |b| = a + b

(2) a > b

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Statement (3) Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

Statement (4) EACH statement ALONE is sufficient.

Statement (5) Statements (1) and (2) TOGETHER are NOT sufficient.

I tried to solve this question as (a+b)^2 > ab but was not able to reach the correct ans ?
Really could use some help from experts

Thanks
Teja
[spoiler]ans:1[/spoiler]


[/quote][/spoiler]
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by MartyMurray » Tue Dec 23, 2014 6:12 pm
evs.teja wrote:Hii, this is a MGMAT mock question. Please don't forget to explain your approach

If ab ≠ 0 and a + b ≠ 0, is 1/(a+b)< 1/a + 1/b ?

(1) |a| + |b| = a + b

(2) a > b

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Statement (3) Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

Statement (4) EACH statement ALONE is sufficient.

Statement (5) Statements (1) and (2) TOGETHER are NOT sufficient.

I tried to solve this question as (a+b)^2 > ab but was not able to reach the correct ans ?
Really could use some help from experts

Thanks
Teja
[spoiler]ans:1[/spoiler]
I did it this way.

First, from the question, you can tell that neither a nor b can be 0.

Then I went directly to the statements to see what the deal is.

Looking at Statement 1, I figure out that for |a| + |b| = a + b, it has to be the case |a|= a and |b| = b. If a and b are not 0, this means they are both positive.

Go back to the question and try some positive numbers.

First try 1 for both a and b, and find this. 1(1 + 1) < 1/1 + 1/1 or 1/2 < 2

Then try 3 for both a and b, and find this. 1/(3 + 3) < 1/3 + 1/3 or 1/6 < 2/3

Now that I have seen it for more clearly, I realize that if a and b are both positive, 1/(a+b) is always less than 1/a, and 1/(a + b) is always less than 1/b. So, 1/(two positive numbers added together) is always less than 1/(one of the numbers) or 1/(the other number) and is certainly less than 1/(one of them) + 1/(the other).

Sufficient.

Now we look at Statement 2.

a or b or both could be positive or negative. So we can't tell which side of the equation in the question would be greater.

Insufficient.

Choose A.
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by evs.teja » Thu Dec 25, 2014 5:59 am
Dear Marty Murray,

Am I allowed to solve the question after converting into the form (a+b)^2 > ab ?

If yes, then statement A is not sufficient coz its failing for values 0.2 and 0.3.

If no, then why not.

Please explain


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Teja
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by [email protected] » Thu Dec 25, 2014 8:55 am
Hi evs.teja,

Can you explain what you mean when you say that "statement A....its failing..."?

Whether you use positive integers or positive decimals, the answer to the question is still ALWAYS YES, so Fact 1 is SUFFICIENT.

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by evs.teja » Fri Dec 26, 2014 2:20 am
Hi Rich,

I got the answer ;)

In the question I remodified this equation 1/a+b > 1/a + 1/b to (a+b)^2 > ab while solving.

For statement A when I use the nos 0.2 and 0.3 for this eqn i.e. (a+b)^2 > ab I thought it was failing because (0.2 +0.3)^2 is 0.25 which is correct and butI miscalculated 0.2 *0.3 which is 0.06 and I took it as 0.6 and concluded this equation not getting satisfied.

After going through your explanation I was wondering that why was I not getting the ans with the modified equation as it was also the same.

So my intent in posting this question was, in general, whether you are allowed to modify the equation a little as per your convenience.

I take the answer now as yes( right ?)


Sorry for the inconvenience.


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Teja
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by [email protected] » Fri Dec 26, 2014 8:57 am
Hi Teja,

In many DS questions, you CAN rewrite/modify the given question; that "step" can often make the question easier to answer. You just have to make sure that you're not inadvertently changing the question and missing some of the possibilities. Pay careful attention to situations in which variables appear in the denominator of a fraction - those variables might be positive OR negative values, so cross-multiplying or dividing variables out could end up removing an answer.

For example: Does "N^3 = N?"

There are 3 "YES" answers to this question (N = -1, 0 and 1).

If you change the question by dividing both sides by "N", then it becomes "Does N^2 = 1?"

There are now ONLY 2 "YES" answers to this question (N = -1, 1), Missing the "0" would likely cost you this question.

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