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Eggs are sold in packages of six or eleven only. If Doris bought 70 eg

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Bunuel
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Eggs are sold in packages of six or eleven only. If Doris bought 70 eg [#permalink] New post   05 Jul 2016, 12:27
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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.
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B
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Re: Eggs are sold in packages of six or eleven only. If Doris bought 70 eg [#permalink] New post   05 Jul 2016, 12:54
No strategy involved. Simple question demanding fast calculation.

11x2 = 22 => 70-22=48 => 48/6 is an integer
Ans B. 2.

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Re: Eggs are sold in packages of six or eleven only. If Doris bought 70 eg [#permalink] New post   05 Jul 2016, 21:20
Bunuel wrote:
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.


Let number of packs of six = s
let number of packs of eleven = e
6s + 11e = 70
Now , we need to test for values of e .
Since sum 70 is even and 6s will always be even , e can't be odd .
Now , we can test for values e = 2 , 4 and 6
11*2 + 6*8 = 22 + 48 = 70
Answer B
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Re: Eggs are sold in packages of six or eleven only. If Doris bought 70 eg [#permalink] New post   05 Jul 2016, 22:26
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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Re: Eggs are sold in packages of six or eleven only. If Doris bought 70 eg [#permalink] New post   06 Jul 2016, 06:31
Bunuel wrote:
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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Re: Eggs are sold in packages of six or eleven only. If Doris bought 70 eg [#permalink] New post   28 Jun 2017, 08:50
Bunuel wrote:
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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Eggs are sold in packages of six or eleven only. If Doris bought 70 eg [#permalink] New post   28 Jun 2017, 09:56
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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Re: Eggs are sold in packages of six or eleven only. If Doris bought 70 eg [#permalink] New post   30 Jun 2017, 09:25
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Bunuel wrote:
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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Re: Eggs are sold in packages of six or eleven only. If Doris bought 70 eg [#permalink]
30 Jun 2017, 09:25
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