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

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Of the diplomats who attended a summit conference: 20 spoke French, 32 [#permalink]

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New post 09 Jul 2015, 04:08
3
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A
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D
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Difficulty:

  25% (medium)

Question Stats:

82% (01:58) correct 18% (03:07) wrong based on 225 sessions

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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

Kudos for a correct solution.
Spoiler: OA

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Re: Of the diplomats who attended a summit conference: 20 spoke French, 32 [#permalink]

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New post 09 Jul 2015, 04:58
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2
Bunuel wrote:
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

Kudos for a correct solution.


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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image.jpg [ 37.25 KiB | Viewed 2148 times ]

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Of the diplomats who attended a summit conference: 20 spoke French, 32 [#permalink]

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New post 09 Jul 2015, 05:14
2
Bunuel wrote:
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

Kudos for a correct solution.


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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File comment: www.GMATinsight.com
Sol 6.jpg
Sol 6.jpg [ 181.79 KiB | Viewed 2117 times ]


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Re: Of the diplomats who attended a summit conference: 20 spoke French, 32 [#permalink]

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New post 13 Jul 2015, 02:28
1
Bunuel wrote:
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

Kudos for a correct solution.


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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Of the diplomats who attended a summit conference: 20 spoke French, 32 [#permalink]

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New post 03 Aug 2015, 09:20
1
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
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Re: Of the diplomats who attended a summit conference: 20 spoke French, 32 [#permalink]

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New post 03 Aug 2015, 20:36
1
Bunuel wrote:
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

Kudos for a correct solution.


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)
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Re: Of the diplomats who attended a summit conference: 20 spoke French, 32 [#permalink]

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New post 21 Jan 2018, 20:03
Bunuel wrote:
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


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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Re: Of the diplomats who attended a summit conference: 20 spoke French, 32   [#permalink] 21 Jan 2018, 20:03
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