Of the diplomats attending a summit conference, 20 speak French, 32 do not speak Russian, and 20% of the diplomats speak neither French nor Russian. If 10% of the diplomats speak both languages, then how many diplomats attended the conference?

A. 72
B. 96
C. 108
D. 120
E. 150
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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

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

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

Answer: Option 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

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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