A team of 2 is to be selected from a group of 5. if the number of male

Question

A team of 2 is to be selected from a group of 5. if the number of males in the group is n, then what's the value of n?

(1) The number of males in the group is one more than the number of females
(2) The probability the team consists of at least one male is 9/10

Nidzo · Answer

1) Only way this is possible with 5 people is if there are 3 men and 2 woman.

n = 3

SUFFICIENT

2) If the probability for the team to have at least one man is  \frac{9}{10} , then the probability of selecting only women is  \frac{1}{10}

Let the number of women in the group be x.

\frac{x}{5}*\frac{x-1}{4} = \frac{1}{10}

\frac{x^2-x}{20} = \frac{2}{20}

x^2 - x = 2

x^ - x - 2 = 0

(x - 2)(x + 1)

x = 2 or x = -1

As x cannot be negative, x = 2. If there are 2 women in a group of 5 people, then 3 are men.

n = 3

SUFFICIENT

Answer D

arya251294 · Answer

Statement 1   is straight forward
it gives us a relation between males and females
if there are n males then there are 5-n females

we are given that n = 5-n + 1
therefore, n = 3

Sufficient.

Statement 2

The probability that the team consists of at least one male = 1 - the probability that the team consists of no male,
which is equal to 
P(at least one male) =  1 -   = 9/10  (No male means choosing both team members from the set of females.)

If we calculate this, we will get n = 3
We don't have to calculate it though, we can confidently say that this statement is also sufficient.

Therefore answer - D

luisdicampo · Answer

Deconstructing the Question

We need the value of   n  , the number of males in a group of   5  .

So the number of females is   5-n  .

This is a Data Sufficiency question, so the goal is to determine whether each statement gives one unique value of   n  .

The key ideas are direct translation in statement (1) and complement counting in statement (2).

Step-by-step

From the question stem, males are   n   and females are   5-n  .

Statement (1) : The number of males in the group is one more than the number of females.

This gives:

n=(5-n)+1

So:

n=6-n

2n=6

n=3

This gives one unique value of   n  .

Statement (1):  Sufficient

Statement (2) : The probability the team consists of at least one male is   \frac{9}{10}  .

Use the complement.

If the probability of at least one male is   \frac{9}{10}  , then the probability of all females is:

1-\frac{9}{10}=\frac{1}{10}

The total number of 2-person teams from 5 people is:

\frac{5!}{2!3!}=10

So the number of all-female teams must be   1  .

If there are   5-n   females, then:

\frac{(5-n)!}{2!(3-n)!}=1

The number of ways to choose 2 people is 1 only when there are exactly 2 females.

So:

5-n=2

n=3

This also gives one unique value of   n  .

Statement (2):  Sufficient

Answer: D

A team of 2 is to be selected from a group of 5. if the number of male

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GMAT Data Sufficiency (DS) Questions

A team of 2 is to be selected from a group of 5. if the number of male

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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Perfect 805 Score Debrief by Julia

My Rewards