Data Sufficiency

gmat1011 wrote:Stuart -

Is there any trick to get some idea as to whether a quadratic equation will get you + numbers or non square root numbers as an answer...

In the bulbs question, if we were to set up the quad equations for 1 and 2 and solve and finally arrive at 3 for each, it took me a good 3.5 minutes!

The thing is sometimes after solving you get two negative numbers or something and you are forced to conclude that the stem is insufficient.... so I am not always 100 pc sure as to whether I can merely rely on the ability to set up quad equations as an indicator for sufficiency

Since you mentioned: data sufficiency Grandmasters don't need to set up equations; just want to know what grandmasters look for to recognize that solvable equations for both statements can be set up... Any practical pointers wrt quad equations vs. ability to recognize sufficiency would be greatly appreciated!!

Many thanks....

Once you write the equation in x^2 + ax + k = 0 form, the only thing you need to look at is the sign in front of the constant.

If k is positive, then both solutions will have the same sign; if k is negative, then both solutions will have different signs.

dream700 wrote:@ Stuart Kovinsky

The qn does state that Two bulbs are to be drawn simultaneously...

hence, I guess the order their defect will not matter...


Deutsch750

As I posted above, it's irrelevant whether they're drawn simultaneously or sequentially - the math works out exactly the same.

Even if you draw them simultaneously, there are two things that can happen:

bulb 1 defective, bulb 2 non defective; and
bulb 1 non defective, bulb 2 defective.

Our solution has to account for both of these possibilities.

thanks stuart!

gmat1011 wrote:Stuart -

Is there any trick to get some idea as to whether a quadratic equation will get you + numbers or non square root numbers as an answer...

In the bulbs question, if we were to set up the quad equations for 1 and 2 and solve and finally arrive at 3 for each, it took me a good 3.5 minutes!

The thing is sometimes after solving you get two negative numbers or something and you are forced to conclude that the stem is insufficient.... so I am not always 100 pc sure as to whether I can merely rely on the ability to set up quad equations as an indicator for sufficiency

Since you mentioned: data sufficiency Grandmasters don't need to set up equations; just want to know what grandmasters look for to recognize that solvable equations for both statements can be set up... Any practical pointers wrt quad equations vs. ability to recognize sufficiency would be greatly appreciated!!

Many thanks....

There is no haziness in GMAT questions. For instance, if your variable represents a number of things, it got to be a positive integer only. Even if you end up getting a quadratic in that variable, at least one root of it is got to be a positive integer. Now, what grandmasters according to Stuart can predict is all about the nature of roots of the quadratic in hand.

Stuart's this equation
n/10 * (n-1)/9 = 1/15

is seen by the Grandmasters as in the form

a x^2 - b x - c = 0

for some positive a, b, and c; and they conclude that since the product of roots is negative, one root is positive (which is got to be a positive integer in the present case), and the other negative (this we don't need to consider in the present case).

Hence, just by observation and deduction, the Grandmasters call it sufficient. But, if the quadratic is not in the form

a x^2 - b x - c = 0,

rather it's in the form

a x^2 - b x + c = 0

for some positive a, b, and c; then they conclude that both the sum and product of roots of this quadratic are positive and at least one root of it is got to be a positive integer, but it's still not sufficient until they are sure that the other positive root is not an integer, which again won't take them another mile to go if they really are data sufficiency Grandmasters according to Stuart.



A box contains 10 light bulbs, fewer than half of which are defective. Two bulbs are to be drawn simultaneously from the box. If n of the bulbs in the box are defective, what is the value of n?

(1) The probability that the two bulbs to be drawn will be defective is 1/15.

(2) The probability that one of the bulbs to be drawn will be defective and the other will not be defective is 7/15.

Good(G) + Defective(D) = 10

D can be 0, 1, 2, 3, 4

G can be 10, 9, 8, 7, 6 respectively

Statement 1: The probability that the two bulbs to be drawn will be defective is 1/15

The probability of first bulb being defective = D/10 and

The probability of Secnd bulb being defective = (D-1)/9

i.e. Probability that both defective = D(D-1)/10x9 = 1/15 i.e. D(D-1) = 6

i.e. D = 3 Sufficient



Statement 2: The probability that one of the bulbs to be drawn will be defective and the other will not be defective is 7/15

The probability of first bulb being defective = D/10 and

The probability of Second bulb NOT being defective = (10-D)/9

i.e. Probability that one of two is defective = D(10-D)/10x9x2! = 7/15 i.e. D(10-D) = 21 but 3 x 7 = 21

i.e. D = 3 Sufficient

Answer: Option D

Prosper!!!