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Eunice sold several cakes. If each cake sold for either

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B
Joined: 19 Sep 2016
Posts: 8

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Location: Thailand
Concentration: Real Estate, Entrepreneurship
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Re: Eunice sold several cakes. If each cake sold for either [#permalink]

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New post 18 Dec 2016, 02:42
gmat1220 wrote:
How about this? Write the cases and apply the unit digit test?

5 sets of (a,b) values

(2,6) --- Unit digit 4 + 4 = 8
(3,5) ---- Unit digit 1 + 5 = 6
(4,4) ----OUT too high
(5,3) ---- Unit digit 5 + 7 = 12 i.e. 2
(6,2) ---- Unit digit 2 + 8 = 10 i.e. 0--------------> Voila!

subhashghosh wrote:
Answer is B.

I was thinking perhaps it can be like, say a multiple of 19 and a multiple of 17 that add up to 0 in unit's place, so by only checking the unit's place i got 38 (19*2) and 102 (17*6). Opinions ?


I would use the same "Unit Digit" approach.
Though, without taking A into consideration, how can you assume the total number of cakes are 8 though?

Or are we essentially taking info from A and just to try if there is only 1 combination for condition B?

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Re: Eunice sold several cakes. If each cake sold for either [#permalink]

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New post 23 Mar 2017, 22:59
Hello Friends,
My 2 cents...

In such scenarios i cheat: i use S-1 info in S-2 and try to solve - if i am able to solve viola we have to answer otherwise NOT

For example, here - we know that a + b = 8 and we need to find b therefore a = 8 -b in other equation:
a = 17 cents
b = 19 cents
17a+19b = 140
17*(8-b) + 19b = 140
136 - 17b + 19b = 140
2b = 4
b = 2 | we have our answer!!!

PLEASE NOTE: i ONLY do it in such scenarios as usually we SHOULD NOT carry data from S-1 to S-2.

Kudos [?]: 54 [0], given: 962

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Re: Eunice sold several cakes. If each cake sold for either [#permalink]

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New post 23 Mar 2017, 23:00
fluke wrote:
Eunice sold x $17 cakes
Eunice sold y $19 cakes

A. Eunice sold 8 cakes. Those cakes can be all 17$ cakes or all $19 cakes. Not sufficient.

B.
17x+19y = 140

Whenever we get such type of questions and we know that x and y can only be integers, it is a must we try all integral values for x and y that may satisy the equation.

Write multiples of 19 that are less than 140; 0,19,38,57,76,95,114,133

Start with x=0;
x=0; 19y = 140-0 = 140; not a multiple of 19.
x=1; 19y = 140-17=123; not a multiple of 19.
x=2; 19y = 140-34=106; not a multiple of 19.
x=3; 19y = 140-51=89; not a multiple of 19.
x=4; 19y = 140-68=72; not a multiple of 19
x=5; 19y = 140-95=55; not a multiple of 19
x=6; 19y = 140-112=38; is a multiple of 19
x=7; 19y = 140-129=11; not a multiple of 19
x=8; 19y = 140-146=-6; not a multiple of 19 and < 0. We can stop here.

We see that the above equation satisfies only for x=6; y=38/19=2;
Sufficient.

Ans: "B"

I wonder if there is an easier way to find this one!!!



Hello Friends,
My 2 cents...

In such scenarios i cheat: i use S-1 info in S-2 and try to solve - if i am able to solve viola we have to answer otherwise NOT

For example, here - we know that a + b = 8 and we need to find b therefore a = 8 -b in other equation:
a = 17 cents
b = 19 cents
17a+19b = 140
17*(8-b) + 19b = 140
136 - 17b + 19b = 140
2b = 4
b = 2 | we have our answer!!!

PLEASE NOTE: i ONLY do it in such scenarios as usually we SHOULD NOT carry data from S-1 to S-2.

Kudos [?]: 54 [0], given: 962

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Joined: 27 Aug 2014
Posts: 58

Kudos [?]: 6 [0], given: 6

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Concentration: Strategy, Technology
GMAT 1: 660 Q45 V35
GPA: 3.66
WE: Consulting (Consulting)
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Re: Eunice sold several cakes. If each cake sold for either [#permalink]

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New post 29 Mar 2017, 18:23
The way I looked at it -

1) Not enough but true
2) we need 17x + 19y = 140.

I was going to check for (x*7)+(x*9) = 0, only one combination worked. Tried it out and it worked. So hence B.

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Re: Eunice sold several cakes. If each cake sold for either [#permalink]

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New post 10 Nov 2017, 08:37
this is never an official problem

in og, we meet similar but different problem, in which oa is b but

it is a very simple math to find that there is one couple x,y which meet choice B.

we never have to do a lot of computation like in this problem.

Kudos [?]: 10 [0], given: 365

Re: Eunice sold several cakes. If each cake sold for either   [#permalink] 10 Nov 2017, 08:37

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