A training program has a roster that includes only advanced students

Question

A training program has a roster that includes only advanced students and beginner students. If the probability of randomly selecting an advanced student from the roster is 5/6, how many advanced students must be added to the roster so that the probability of randomly selecting an advanced student becomes 7/8?

(1) There are 44 more advanced students than beginner students.

(2) The ratio of advanced students to beginner students is 5 to 1.

Bunuel · Accepted Answer

GMAT Club Official Solution:

A training program has a roster that includes only advanced students and beginner students. If the probability of randomly selecting an advanced student from the roster is 5/6, how many advanced students must be added to the roster so that the probability of randomly selecting an advanced student becomes 7/8?

Since the probability of randomly selecting an advanced student from the roster is 5/6, there are 5 advanced students for every 1 beginner student. So, advanced : beginner = 5x : x.

(1) There are 44 more advanced students than beginner students.

This implies that 5x - x = 44. Thus, x = 11, so there are 55 advanced students and 11 beginner students. We now know everything there is to know here, so we can answer the question.

Sufficient.

(2) The ratio of advanced students to beginner students is 5 to 1.

We already know this from the stem, so statement (2) adds no new information and is useless.

Not sufficient.

Answer: A.

vasu1104 · Answer

say 
advanced students= x
beginner students = y
total = x+y

probability of getting advanced students = 5/6

x/x+y = 5/6
we get, x=5y

that means advanced = 5y and beginner = y

we need to add p more students so that probability of getting advanced is 7/8

5y+p/6y+p = 7/8
p=2y

we need to find simply P.

S-1
5y= 44+y
y = 11
sufficient.

S-2
5y:y = 5:1

this is what we already have.
insufficient.

chocie A

SS990 · Answer

Given: P(A=1) 5/6 so P(B=1) =1/6

To find: A to be added so P(A=1)=7/8

1) A=B+44 so A/A+B=5/6 can be solved for A and B hence we would know how much to increae Aby, to get 7/8. Hence sufficient

2) A/B=5/1..but we dont know the aboslute value of A or B or total so this is insufficient.

Hence answer is A

BongBideshini · Answer

\frac{A}{A+B}=\frac{5}{6}
=>\frac{A}{B}=\frac{5}{1}
 
Let, A=5x and B=x
And let "a" advanced students be added 
new ratio,
 \frac{A'}{B'} =\frac{(5x+a)}{x} =\frac{7}{1} 
So, 2x = a

Statement I, 
5x - x = 44
4x = 44
x = 11
So, a = 22.
 Sufficient

Statement II  is already implied by the question stem.
 Insufficient

Ans A

Edskore · Answer

The trap here is sneaky. Statement (2) looks like it's giving you new information — but it's literally just restating what the stem already told you.

When you're told P(selecting advanced) = 5/6, that means for every 6 students, 5 are advanced and 1 is a beginner. In other words, advanced:beginner = 5:1. Statement (2) says advanced:beginner = 5:1. That's... the same thing. Completely redundant. If you pick C or D here, you fell for it.

Set up the stem properly first:

1. Let advanced = 5k, beginner = k (since ratio is 5:1)
2. We need to find "a" — the number of advanced students to add so that (5k + a)/(6k + a) = 7/8

Cross-multiplying: 8(5k + a) = 7(6k + a)
40k + 8a = 42k + 7a
a = 2k

So we just need to find k to get a.

Statement (1): advanced - beginner = 44
5k - k = 44
4k = 44
k = 11

So a = 2(11) = 22. We can answer the question. Sufficient.

Statement (2): advanced:beginner = 5:1. Already knew this. Not sufficient.

Answer: A

The bigger lesson is about DS trap recognition. The GMAT sometimes embeds the same info in the stem and one of the statements. If you don't fully simplify the stem first, you'll think Statement (2) is telling you something new. I got burned by this pattern early in my prep, and now I always check: does this statement actually add information that wasn't already implied?

Anytime P(some group) = p/q in a DS stem, you've already locked in the ratio. Any statement that gives you "the ratio is X:Y" is likely redundant.

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A training program has a roster that includes only advanced students

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