A list of possible transplant patients contains people who can accept

Question

A list of possible transplant patients contains people who can accept A, B, or O positive type blood. 12 of the people can receive only type O blood, but 17 people can accept either type O or type B blood. All of the people who can accept type A blood can also accept type O, while anyone receiving either type A or type B blood cannot receive the other type. If there are 92 people on the list, and 14 of them can accept type A blood, how many people can only accept type B blood?

A. 63
B. 49
C. 35
D. 32
E. 26

Show Answer

Official Answer

B

A. 63
B. 49
C. 35
D. 32
E. 26

karthik07 · Answer

Since anyone receiving either type A or type B blood cannot receive the other type ,
14 of them can accept type A blood+12 of the people can receive only type O blood+ 17 people can accept either type O or type B blood,
people who can only accept type B blood=92-(14+12+17)=49 
Ans is B

nightblade354 · Answer

Here's my 2 cents, I do not know if it'll help. This was a tricky question to think about, and I certainly hope it is not on the real GMAT!

Each group is its own subgroup and DO NOT overlap.

1. Only O: nothing else. They cannot accept any other blood.

2. A and O: Cannot accept B, so it cannot overlap with B or O (because they are unique). 
 --- What about only A? all of A can accept O

3. B and O: Cannot accept A, so it cannot overlap with A or O (because they are unique). Not all of B can accept O, so we need a new category to fill the remaining members
 4. ---- What about only B? This is missing from our given information!

So, if you total them up: 12 + 14 + 17 = 43 thus far

92 - 43 = 49 missing participants!

abhimahna · Answer

Hi  TheMastermind  ,

Here I go:

We are given :

Only O: 12 ==> They can not have A or O
A and O : 14 ==> They cannot have B + They cannot be Only O or Only A.
B or O: 17 ==> They can accept any of B or O. They cannot be A + they cannot be only O + they cannot be only B.

(I know B or O might be confusing you. If I am saying my body can accept either B or O blood group, that doesn't mean my body can accept only B or Only O.)

Total: 92

Therefore, Only B = Total - all the other groups given

==> Only B = 92 - (12+14+17) = 49.

Does that make sense?

mariekondo · Answer

I attempted it like this:

Each of the groups are exclusive; transplant patients can be categorised into what they can receive:

A: We know all A can receive O
B: Here is what we're looking for
AB: A cannot receive B and vice versa
ABO: A cannot receive B and vice versa
AO: We know all A can receive O
BO: We know that some can receive B and O
O: We know that some can only receive O

Hence:

Groups A and AO can be grouped together: 14 patients
Groups AB, ABO cannot exist: 0 patients
Group BO: 17 patients
Group O: 12 patients
Group B: 92 -14 -17 -12 = 49 patients

the wording of the question made it very tricky to understand!

A list of possible transplant patients contains people who can accept

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A list of possible transplant patients contains people who can accept

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