There are 125 members in the winter sports club. Of those, 20 do not

Question

There are 125 members in the winter sports club. Of those, 20 do not ski or snowboard. If 1/3 of the people who ski also snowboard, and if the number of people who only snowboard is equal to 1/2 of the number of people who ski and snowboard, how many people only snowboard?

A. 15
B. 20
C. 30
D. 45
E. 60

A. 15
B. 20
C. 30
D. 45
E. 60

shobhitsingh309 · Answer

Let 3x people ski. So 2x people only ski and x people ski and snowboard. Now x/2 people only snowboard.
Out of 125 people, 20 do not participate. So only 105 remain.
So, 2x+x+x/2=105
So, x=30
But we need x/2 which is equal to 15.
So the answer is 15.

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Skyline393 · Answer

Call total Ski members = a => No Ski member = 1-a => People who ski & snowboard = a/3 
Who only snowboard = 1/2 * people who ski & snowboard = 1/2 * a/3 = a/6 
People do not ski or snowboard = 20 = 20/125 = 4/25
Total No ski members = People who only snowboard + People do not ski or snowboard => 1- a= a/6 + 4/25 => a = 90. 
Hence, peple who only snowboard = a/60 = 90/6 = 15. Answer A
It is easier to solve by table but I dont know how to attach image so I write down this..

Doer01 · Answer

Using Venn diagram

ScottTargetTestPrep · Answer

We can let k = the number of people who ski, n = the number of people who snowboard, and b = the number of people who do both. From the information given in the problem, we can create the equations:

k + n - b + 20 = 125,

(1/3)k = b,

and

n - b = (1/2)b

n - b = (1/2)(k/3k)

Simplifying the third equation, we have:

n - b = (1/6)k

Substituting ⅙k for n - b in the first equation, we have:

k + (1/6)k + 20 = 125

7/6 k = 105

k = 105 x 6/7

k = 90

Since the number of people who only snowboard is n - b, which is (1/6)k , the number of people who only snowboard is(1/6)(90) = 15.

Answer: A

Kinshook · Answer

Given: 
1. There are 125 members in the winter sports club. Of those, 20 do not ski or snowboard. 
2. 1/3 of the people who ski also snowboard, 
3. the number of people who only snowboard is equal to 1/2 of the number of people who ski and snowboard

Asked: how many people only snowboard?

Total number of people to either ski or snowboard = 125-20=105
 
Let the number of people who ski be 3x
The number of people who only ski= 2x
The number of people who ski and snowboard = x
The number of people who only snowboard = x/2

Since 2x+x+x/2=105
x= 30

x/2 = 15
The number of people who only snowboard = 15

IMO A

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Archit3110 · Answer

solving it in 2x2 matrix

---ski----nski----total
sb--x/3---x/6----x/2
nsb--2x/3---20---2x/3+20
total--x-----125-x---125
solve for x 
x/2+2x/3=105
x= 30
so only SB ; 30/2 ; 15
IMO A

ScottTargetTestPrep · Answer

Solution:
 
We can use the formula:

Total = Ski Only + Snowboard Only + Both + Neither

We can let the number of people who ski = x; therefore, x/3 = the number of people who do both and the number of people who snowboard only = x/6. 
 
125 = (x - x/3) + x/6 + x/3 + 20

105 = 7x/6

630 = 7x

90 = x

Therefore, the number of people who only snowboard is Snowboard Only = x/6 = 15.

Answer: A

Paras96 · Answer

There are 125 members in the winter sports club. Of those, 20 do not ski or snowboard. If 1/3 of the people who ski also snowboard, and if the number of people who only snowboard is equal to 1/2 of the number of people who ski and snowboard, how many people only snowboard?

A. 15
B. 20
C. 30
D. 45
E. 60

Let the no. of members who ski = 6a,
According to the given scenario,
=> the no. of members who ski and snowboard = 2a
=> the no. of members who only snowboard = a

Now, Total members who ski or snowboard = no. of members who ski + no. of members who only snowboard
=> 125 - 20 = 6a + a
=> 105 = 7a
=> a = 15

Hence A

lisahoang1301 · Answer

I think a table would give better visibility:
Let x be the number of people who ski (including both only ski and ski & snowboard):
    
 Ski 
 No Ski 
 Total 
 
  Snowboard 
 x* \frac{1}{3}  
 x* \frac{1}{3} * \frac{1}{2}

No Snowboard 
  
 20

Total 
 x 
 125-x 
 125

So we have an equation and solve for x:
x* \frac{1}{3} * \frac{1}{2}  + 20 = 125-x
x=90

--> So number of people who only snowboard is 90* \frac{1}{3} * \frac{1}{2}  =15

There are 125 members in the winter sports club. Of those, 20 do not

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	Ski	No Ski	Total
Snowboard	x*\(\frac{1}{3}\)	x\(\frac{1}{3}\)\(\frac{1}{2}\)
No Snowboard		20
Total	x	125-x	125

GMAT Problem Solving (PS) Questions

There are 125 members in the winter sports club. Of those, 20 do not

Prep Toolkit

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