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2

6x+11y=70

we need to find y in above equation => y=70-6x/11

only value for x where y is integer is x=8.
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Bunuel
Eggs are sold in packages of six or eleven only. If Doris bought 70 eggs exactly, what could be the number of large packs Doris bought?


A. 6.
B. 2.
C. 3.
D. 5.
E. 4.

Number os large packs must be even so that when even number is subtracted from 70, we get an even number (even number is needed to be divided by 6). C and D are out.

Let's check option B.

If he has 2 packs of large eggs, i.e. 22 eggs, then he has 70-22= 48 eggs, which is a multiple of 6.

Hence B is the answer
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Bunuel
Eggs are sold in packages of six or eleven only. If Doris bought 70 eggs exactly, what could be the number of large packs Doris bought?


A. 6.
B. 2.
C. 3.
D. 5.
E. 4.
Hey Bunuel could you please provide a more logical approach. I know, you're the expert. :)
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If x is the number of six egg packages
If y is the number of eleven egg packages
6x + 11y = 70(from question stem)

The only number, which will give 70 is when x=8 and y=2.

If you use y(to be any of the other answer options i.e. 3,4,5,6)
it is not possible to get an integer value for x.

Hope that helps!
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Bunuel
Eggs are sold in packages of six or eleven only. If Doris bought 70 eggs exactly, what could be the number of large packs Doris bought?


A. 6.
B. 2.
C. 3.
D. 5.
E. 4.

We can let x = the number of large packs and y = the number of small packs; thus:

11x + 6y = 70

6y = 70 - 11x

y = (70 - 11x)/6

We see that 6 must evenly divide (70 - 11x). Thus, of our answer choices, x could be 2.

Answer: B
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