Of the 200 stamps in a collection, 70 are foreign and 50 are more than

Question

Of the 200 stamps in a collection, 70 are foreign and 50 are more than 10 years old. If 20 stamps are both foreign and more than 10 years old, how many stamps are neither foreign nor more than 10 years old?

A. 30
B. 80
C. 100
D. 130
E. 150

Show Answer

Official Answer

C

A. 30
B. 80
C. 100
D. 130
E. 150

BrushMyQuant · Answer

Lets make a 2x2 table

<=10 yrs >10yrs
Foreign a 20 70
Non-Foreign c d e 
 f 50 200

a + c = f
20 + d = 50 => d = 30 
a + 20 = 70 => a = 50
c + d = e
f + 50 = 200 => f = 150
70 + e = 200 => e = 130

So, the question is asking us the value of c
a + c = f and we know that a = 50 and f = 150
so, c = 100

So, answer will be C.
(please update the OA)

Hope it helps!

EMPOWERgmatRichC · Answer

Hi gmatmania17,

nkdotgupta is describing the Tic-Tac-Toe Board approach to Overlapping Sets questions; I'm a big fan of this approach since it helps solve both standard and "quirky" versions of this type of prompt. Since this question asks us to deal with the standard terms in an Overlapping Sets question, you COULD use the following formula to answer it:

Total = Group A + Group B - Both + Neither

Group A = Foreign stamps
Group B = More than 10 years old
Both = BOTH Foreign and More than 10 years old
Neither = NEITHER Foreign NOR More than 10 years old

200 = 70 + 50 - 20 + Neither

200 = 100 + Neither
100 = Neither

So, the number of stamps that are NEITHER Foreign NOR More than 10 years old is 100

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

gmatmania17 · Answer

Thank you very much to both users!! Nktdotgupta what do you mean by changing the OA? What is the OA?

EMPOWERgmatRichC · Answer

Hi gmatmania17,

The included answers/explanations are correct. When it was originally posted, the correct answer must have been either missing or incorrect (as noted, Bunuel has taken care of the issue).

GMAT assassins aren't born, they're made,
Rich

PareshGmat · Answer

Answer = C. 100 Refer diagram below: Calculated using double matrix method oed.png Black >> Information given Red/Orange >> Calculated

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Of the 200 stamps in a collection, 70 are foreign and 50 are more than

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