A school has 3 classes, math class has 14 students. English class has 10 students, PE class has 11 students. There are 20 students taking only one class, 3 students are taking all three classes. How many students are taking two classes?
A) 6
B) 3
C) 9
D) 18
I personally think it's A
What do you guys think?
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Over lapping problem......again, kinda tricky
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Mr.Hollywood
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Mike@Magoosh
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Hi, there. I'm happy to help with this. 
First of all, I'll say: this question is unusual in form, because GMAT PS questions invariably have 5 answer choices. Also, the numbers seem a bit smaller and simpler than I've seen on analogous GMAT questions. Also, on the real GMAT, answer choices are almost always in numerical order. I am suspicious of the source of these questions.
A school has 3 classes, math class has 14 students. English class has 10 students, PE class has 11 students. That's a sum of 14 + 10 + 11 = 35. This sum counts "doublers" twice, and counts "triplers" three times.
There are 20 students taking only one class. Remove the singletons, 35-20 = 15, and that number represents the doublers counted twice and the triplers counted three times.
3 students are taking all three classes. There are three triplers, so they count for 9 in the total. 15 - 9 = 6, which represents the doublers counting twice. That means, there must be 3 doublers.
Answer = B
Does all this make sense? Please let me know if you have any questions on what I've said.
Mike
First of all, I'll say: this question is unusual in form, because GMAT PS questions invariably have 5 answer choices. Also, the numbers seem a bit smaller and simpler than I've seen on analogous GMAT questions. Also, on the real GMAT, answer choices are almost always in numerical order. I am suspicious of the source of these questions.
A school has 3 classes, math class has 14 students. English class has 10 students, PE class has 11 students. That's a sum of 14 + 10 + 11 = 35. This sum counts "doublers" twice, and counts "triplers" three times.
There are 20 students taking only one class. Remove the singletons, 35-20 = 15, and that number represents the doublers counted twice and the triplers counted three times.
3 students are taking all three classes. There are three triplers, so they count for 9 in the total. 15 - 9 = 6, which represents the doublers counting twice. That means, there must be 3 doublers.
Answer = B
Does all this make sense? Please let me know if you have any questions on what I've said.
Mike
Magoosh GMAT Instructor
https://gmat.magoosh.com/
https://gmat.magoosh.com/
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Mr.Hollywood
- Senior | Next Rank: 100 Posts
- Posts: 34
- Joined: Mon Oct 24, 2011 2:04 pm
- Thanked: 1 times
Thank you it's great. Although I'm not so sure about the "This sum counts "doublers" twice" part. Can you demonstrate a little further regarding the doublers? I do understand the triplers.Mike@Magoosh wrote:Hi, there. I'm happy to help with this.
First of all, I'll say: this question is unusual in form, because GMAT PS questions invariably have 5 answer choices. Also, the numbers seem a bit smaller and simpler than I've seen on analogous GMAT questions. Also, on the real GMAT, answer choices are almost always in numerical order. I am suspicious of the source of these questions.
A school has 3 classes, math class has 14 students. English class has 10 students, PE class has 11 students. That's a sum of 14 + 10 + 11 = 35. This sum counts "doublers" twice, and counts "triplers" three times.
There are 20 students taking only one class. Remove the singletons, 35-20 = 15, and that number represents the doublers counted twice and the triplers counted three times.
3 students are taking all three classes. There are three triplers, so they count for 9 in the total. 15 - 9 = 6, which represents the doublers counting twice. That means, there must be 3 doublers.
Answer = B
Does all this make sense? Please let me know if you have any questions on what I've said.
Mike
GMAT/MBA Expert
-
Mike@Magoosh
- GMAT Instructor
- Posts: 768
- Joined: Wed Dec 28, 2011 4:18 pm
- Location: Berkeley, CA
- Thanked: 387 times
- Followed by:140 members
OK, let's be concrete.Mr.Hollywood wrote:Thank you it's great. Although I'm not so sure about the "This sum counts "doublers" twice" part. Can you demonstrate a little further regarding the doublers? I do understand the triplers.
Let's say:
A is taking Math
B is taking Math
C is taking English
D is taking PE
E is taking PE
F is taking Math and English
G is taking Math and English
H is taking Math and PE
I is taking Math and PE
J is taking English and PE
K is taking Math, English, and PE
L is taking Math, English, and PE
Here, I have marked the "singletons" in purple, the doublers in green, and the triplers in red.
Who is in Math? A, B, F, G, H, I, K, and L ---> 8 people
Who is in English? C, F, G, J, K, and L ---> 6 people
Who is in PE? D, E, H, I, J, K, and L ---> 7 people
8 + 6 + 7 = 21
That sum of 21 counts the two triplers (K & L) three time --- they are included on all three lines of the sums. The sum of 21 counts the 5 doublers (F, G, H, I, and J) each twice --- each one of those is included on two of the three lines of sums.
Thus (5 singletons) + 2*(five doublers) + 3*(two triplers) = 5 + 2*5 + 3*6 = 21
Does this make sense?
Mike
Magoosh GMAT Instructor
https://gmat.magoosh.com/
https://gmat.magoosh.com/
