Samantha invests i1 dollars in bond X, which pays r1

Well..No one till now commented on the possibility of negative interest rate??

-ve interest rates are not possible for such investment. Do not over generalize the things on gmat.

There are comments on this in two posts above: we are told that "bond X pays r1 percent simple interest annually" so it can't be negative.

Hello Bunuel , Shrouded1 ,
What abt the following consideration .
from (1) we know r1 > r2 so irrespective of i1 being greater or less than i2 , we would know that i1*r1 yields high value .
Example
Consider i1 > i2 (and we know r1 >r2 and i1 and i2 have to be positive values ).
say i1 : 150 , i2 : 100
Value of Inv on X : i1*r1 : 150*5% : 7.5
Value of Inv on Y : i2*r2 : 100*3% : 3
Therefore X > Y
Take the other case of i1< i2 ( and still r1 >r2 and i1 and i2 have to be positive values ).
Say i1 : 100 , i2 : 150
Value of Inv on X : i1*r1 : 100*5% : 5
Value of Inv on Y : i2*r2 : 150*3% : 4.5
So it does not matter what is the principle amount hence (A) or stmnt 1 is sufficient .
Where am I going wrong ?

PS : Gurpreet I have corrected the OA .Sorry abt that .

That's not correct. Are you saying that interest earned depends only on interest rate?

So if I ask you what would you prefer 1% annual interest from $1,000,000,000 or 100% annual interest from $1?

Bunuel, I will be more than happy to accept the former with only 0.25%

I get it now .My choice of plugin numbers was not comprehensive enuf .
Thanks a lot Bunuel .

Nandini, the numbers you have taken in this particular case are playing the trick. In your example, the ratio of the R's and I's are peculiar.

Take extreme example. If you think i1 & i2 do not matter. Do this:

Case 1
i1=$10000 and i2=$100
r1=5% and r2=4.99% .. as a result r1>r2
Value of return ......... X = 10000*5% = $500
Y = 100*4.99% = $4.99
X >> Y

Case 2
i1=$100 and i2=$10000
r1=5% and r2=4.99% .. as a result r1>r2
Value of return ......... X = 100*5% = $5
Y = 10000*4.99% = $499
X << Y

Can the rates R1 and R2 be fractions? In that case R1^2 > R2^2 would not necessarily mean R1>R2.

Actually it would.

For non-negative \(x\) and \(y\) if \(x^2>y^2\), then \(x>y\): since both sides of \(x^2>y^2\) are non-negative we can take the square root from both sides and get \(x>y\).

Adding/subtracting/multiplying/dividing inequalities: help-with-add-subtract-mult-divid-multiple-inequalities-155290.html



Hope it helps.

Is i1r1>i2r2?

Statement 1

ri>r2

This is clearly insufficient

Statement 2

i1/i2>r1/r2

i1r2>r1i2.

Insufficient on its own

Now both together

i1r2>r1i2
r1>r2

Multiplying inequalities since we know both sides are positive then simplifying we get

i2>i2

Since we know that r1>r2 as well then

i1r1>i2r2

Sufficient

C

Hope this helps
Cheers
J

Read to eat stuff: it will refresh your concept and keep you away from any confusion during exam.
Kudos me if it is helpful.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 4 variables (i1, i2, r1 and r2) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) and 2):
Since r1 and r2 are positive, (r1)^2 > (r2)^2 implies r1 > r2 or r1/r2 > 1.
Since i1/i2 > r1/r2 from the condition 2), i1/i2 > r1/r2 > 1 implies i1/i2 > 1 or i1 > i2.
i1 * r1 > i2 * r2.
Thus the interest from the bond X is more than the interest from the bond Y.

Both conditions together are sufficient.

Therefore, C is the answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.