Of the diplomats who attended a summit conference: 20 spoke French, 32

Of the diplomats who attended a summit conference: 20 spoke French, 32 did not speak Russian and 20% of the diplomats spoke neither French nor Russian. If 10% of the diplomats spoke both French and Russian, then how many diplomats attended the conference?

A. 70
B. 96
C. 108
D. 120
E. 150

{Total} = {French} + {Russian} - {Both} + {Neither}

{Total} = 20 + ({Total} - 32) - (0.1*{Total}) + 0.2*{Total}

Solving gives {Total} = 120.

Answer: D.
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2X2 matrix will be the easiest way to calculate this.

Text in black: given statements
Text in red: calculated values


Thus D (120) is the correct answer

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Hello
In the explanation that you gave above for the people who speak Russian through the equation (Total-32), aren't we including the people who speak neither of the two languages. Please clarify if I am wrong. I tried to solve it through double matrix method.

Thanks

Hi vik09,

in the following Equation

{Total} = {French} + {Russian} - {Both} + {Neither}

{Total} = 20 + ({Total} - 32) - (0.1*{Total}) + 0.2*{Total}

Solving gives {Total} = 120.

The Neither of the two languages has been accounted for by 0.2*{Total}

(0.1*{Total}) has been subtracted because It was counted twice in 20 as well as in ({Total} - 32)

I hope it answers your questions.

However the solution by double matrix method is as attached.

Answer: Option

Thanks a lot
Though it's not relevant to this particular question, I need your valuable insights on how should I improve upon P&C and Geometry in particular !! In general in the Quant CAT's that I take on GMAT club I get on an average 9 questions wrong and 90% of these questions are usually from P&C and Geometry. I am targeting a score of Q 50 please help me in this regard.

Regards,
Vikas

Point 1: The tradition of Thanking on GMAT Club is by Pressing the button of +1Kudos

Point 2: P&C is the topic in which a test taker takes any logical approach then can arrive at the right answer but we make various mistakes e.g. taking arrangement into account when not needed or Considering some repeated cases of arrangement due to ignorance of some specific point. The idea of learning P&C is "It's good to make Mistakes" but repeating the similar mistakes is too dangerous. So Identify the mistake, reason out how to correct it rather than just hopping onto another approach to get the right answer.

To improve your skills with P&C you need to identify your mistakes and Understand how to correct the mistake. Taking alternative logic after making a mistake is not a good way to learn.

Point 3: Geometry is a topic that requires some Imagination alongwith the willingness to stick to the limited properties rather than making a Looong list of properties and then getting confused which one to apply. The best way to deal with geometry is "Practice, Practice and Practice"

Starting by filling in what we already know - based on the relationships from the stem.
What we add last is the part right beneath NR.
The column of NR gives an equation which we can solve for x.

ANS D

Make the Matrix as mentioned in figure and [Keep an eye on the colour coding in table as per instruction]

Answer: Option D

800score Official Solution:

Let’s define some variables to make notation easier:
T = Total number of diplomats at the conference.
F = Number who speak French.
R = Number who speak Russian.
B = Number who speak BOTH French and Russian.
N = Number who speak NEITHER French NOR Russian.
To solve this problem, we have to remember not to double count diplomats that speak both languages.

We have a very helpful formula for Set Overlap questions:
Group 1 + Group 2 + Neither – Both = Total.

In this case, our equation becomes:
F + R + N – B = T.

Substituting the given information, we have:
20 + R + 0.2T – 0.1T = T.

We have to think a little bit to put the number of diplomats who speak Russian in terms of the total number of diplomats. Since 32 of the diplomats to do not speak Russian, we know that:
R = T – 32.

Now our equation becomes:
20 + T – 32 + 0.2T – 0.1T = T.

We can solve this for T:
20 + T – 32 + 0.2T – 0.1T = T
0.1T = 12
T = 120.

The correct answer is choice (D).
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I think this question can be solved in a very simple and quick way

We are given No Russian = 32
And let's suppose total = x

32 = French Only + Neither French Nor Russian ---- (1)

French Only = French - Both

French = 20
Both = 0.1x
Neither = 0.2x
Plugging all the values in equation (1) we get

32 = 20-0.1x+0.2x
12=0.1x
x=120

Or one can start with 'Both' since data gives multiples of that.

Say, no of people who speak both = x = 10% of Total
No. of people who speak neither = 20% of Total = 2x
No. of people who speak only French = 20 - x

Those who do not speak Russian = Those who speak neither + Those who speak only French = 2x + (20 - x) = 32
x = 12

Since x = 10% of Total = 12,
Total = 120

Answer (D)

We can let n = total number of diplomats who attended the conference, and use the equation:

Total = speaks French + speaks Russian - speaks both + speaks neither

n = 20 + (n - 32) - 0.1n + 0.2n

n = n - 12 + 0.1n

12 = 0.1n

120 = n

Answer: D
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