Problem Solving

Three friends sit down to eat 14 slices of Pizza. If two friends eat the same number of slices, and the third friend eats two more slices than each of the other two, how many slices are eaten by the third friend.

Here's my thought process:

Three friends sit down to eat 14 slices of Pizza: A + B + C = 14 Slices

If two friends eat the same number of slices: A = B

the third friend eats two more slices than each of the other two: C = (A+B) + 4
I picked four because it says that the third friend eats two more slices than each of the other two, to me that sounds like two more than A and two more than B, which is 4.

I'm wrong. Would I appreciate help. TYIA.

afr114 wrote:Three friends sit down to eat 14 slices of Pizza. If two friends eat the same number of slices, and the third friend eats two more slices than each of the other two, how many slices are eaten by the third friend.

4
6
8
10
12

I've added answer choices, which the GMAT would provide.
We can PLUG IN THE ANSWERS for the number of slices eaten by the 3rd friend.
When the correct answer choice is plugged in, the number eaten by the 3rd friend will be 2 more than the number eaten by each of the other 2 friends.

Answer choice C: 8 slices
Since the remaining 6 slices are split equally by the other 2 friends, the number eaten by each of the other 2 friends = 6/2 = 3.
Difference = 8-3 = 5.
Since the difference is too great, the 3rd friend must eat FEWER slices.
Eliminate C, D and E.

Answer choice B: 6 slices
Since the remaining 8 slices are split equally by the other 2 friends, the number eaten by each of the other 2 friends = 8/2 = 4.
Difference = 6-4 = 2.
Success!

The correct answer is B.

Here's my thought process:

Three friends sit down to eat 14 slices of Pizza: A + B + C = 14 Slices

If two friends eat the same number of slices: A = B

the third friend eats two more slices than each of the other two: C = (A+B) + 4
I picked four because it says that the third friend eats two more slices than each of the other two, to me that sounds like two more than A and two more than B, which is 4.

I'm wrong. Would I appreciate help. TYIA.

The portion in red is incorrect.
C eats 2 more slices than either A or B.
Put another way, A and B each eat 2 fewer slices than C:
A = C-2
B = C-2.

Substituting these equations into A + B + C = 14, we get:
(C-2) + (C-2) + C = 14
3C - 4 = 14
3C = 18
C = 6.

afr114 wrote:Three friends sit down to eat 14 slices of Pizza. If two friends eat the same number of slices, and the third friend eats two more slices than each of the other two, how many slices are eaten by the third friend.

Here's my thought process:

Three friends sit down to eat 14 slices of Pizza: A + B + C = 14 Slices

If two friends eat the same number of slices: A = B

the third friend eats two more slices than each of the other two: C = (A+B) + 4
I picked four because it says that the third friend eats two more slices than each of the other two, to me that sounds like two more than A and two more than B, which is 4.

I'm wrong. Would I appreciate help. TYIA.

The bolded part is where you've gone wrong.

It should be C = A + 2 = B + 2

Had they said "the third friend eats 4 more slices than the other two put together", you would be right.

Solution:
A = B = C - 2
(C-2) + (C-2) + C = 14
3C - 4 = 14
3C = 18
C = 6

Choose B

Cheers