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# At Ivan’s petting zoo, visitors can pay to ride yaks and zebras. A yak

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At Ivan’s petting zoo, visitors can pay to ride yaks and zebras. A yak  [#permalink]

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14 Feb 2017, 01:39
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Difficulty:

35% (medium)

Question Stats:

63% (01:44) correct 37% (01:45) wrong based on 55 sessions

At Ivan’s petting zoo, visitors can pay to ride yaks and zebras. A yak ride costs $91, whereas a zebra ride costs just$28. In how many ways can a visitor spend at total of exactly $703 on yak and/or zebra rides at the petting zoo? A. 0 B. 1 C. 2 D. 3 E. 4 _________________ Senior Manager Joined: 13 Oct 2016 Posts: 367 GPA: 3.98 Re: At Ivan’s petting zoo, visitors can pay to ride yaks and zebras. A yak [#permalink] ### Show Tags 14 Feb 2017, 02:21 2 2 Bunuel wrote: At Ivan’s petting zoo, visitors can pay to ride yaks and zebras. A yak ride costs$91, whereas a zebra ride costs just $28. In how many ways can a visitor spend at total of exactly$703 on yak and/or zebra rides at the petting zoo?

A. 0
B. 1
C. 2
D. 3
E. 4

Hi

91x + 28y = 703

7(13x + 4y) = 703

13x + 4y = 703/7 =/= an integer.

We are adding two multiples if 7, so the resultant also must be a multiple of 7, but 703 is not divisible by 7.

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Re: At Ivan’s petting zoo, visitors can pay to ride yaks and zebras. A yak  [#permalink]

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14 Feb 2017, 04:50
1
since 703 is not divisible by 7,

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Re: At Ivan’s petting zoo, visitors can pay to ride yaks and zebras. A yak  [#permalink]

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14 Feb 2017, 10:49
1
Bunuel wrote:
At Ivan’s petting zoo, visitors can pay to ride yaks and zebras. A yak ride costs $91, whereas a zebra ride costs just$28. In how many ways can a visitor spend at total of exactly $703 on yak and/or zebra rides at the petting zoo? A. 0 B. 1 C. 2 D. 3 E. 4 91y + 28z = 703 If y = 1 , 28z = 612 ( Not divisible by 28 ) If y = 2 , 28z = 521 ( Not divisible by 28 ) If y = 3 , 28z = 430 ( Not divisible by 28 ) If y = 4 , 28z = 339 ( Not divisible by 28 ) If y = 5 , 28z = 248 ( Not divisible by 28 ) If y = 6 , 28z = 157 ( Not divisible by 28 ) If y = 7 , 28z = 66 ( Not divisible by 28 ) Thus, answer will be (A) 0 _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2727 Re: At Ivan’s petting zoo, visitors can pay to ride yaks and zebras. A yak [#permalink] ### Show Tags 15 Feb 2017, 16:17 2 Bunuel wrote: At Ivan’s petting zoo, visitors can pay to ride yaks and zebras. A yak ride costs$91, whereas a zebra ride costs just $28. In how many ways can a visitor spend at total of exactly$703 on yak and/or zebra rides at the petting zoo?

A. 0
B. 1
C. 2
D. 3
E. 4

If we let y = the number of yak rides and z = the number of zebra rides, we can create the following equation:

91y + 28z = 703

Factoring out a 7, we have:

7(13y + 4z) = 703

13y + 4z = 703/7

Since 13y + 4z MUST be an integer, and since 703/7 IS NOT an integer, there is no way that a visitor can ride a zebra and/or yak with exactly 703 dollars.

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Re: At Ivan’s petting zoo, visitors can pay to ride yaks and zebras. A yak  [#permalink]

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15 Feb 2017, 23:25
1
Bunuel wrote:
At Ivan’s petting zoo, visitors can pay to ride yaks and zebras. A yak ride costs $91, whereas a zebra ride costs just$28. In how many ways can a visitor spend at total of exactly $703 on yak and/or zebra rides at the petting zoo? A. 0 B. 1 C. 2 D. 3 E. 4 • The cost to ride a yak =$$$91$$
• The cost to ride a zebra = $$$28$$ • Total amount we can spend =$$$703$$
• Therefore we can write the equation as -
• $$91y + 28z = 703$$
• Where y is the number of times one rides a yak
• and z is the number of times one rides a zebra.

• $$28z$$ is always even, and $$91y$$ + Even = Odd, therefore, we can conclude that y will be odd.

• Therefore, $$y$$ can take the value $$1,3,5$$ and $$7$$

• If we plug in these values in the equation $$91y + 28z = 703$$ we will find that none of the above 4 values gives us an integer value of z.

• Hence there are $$0$$ ways.

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Saquib
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Re: At Ivan’s petting zoo, visitors can pay to ride yaks and zebras. A yak &nbs [#permalink] 15 Feb 2017, 23:25
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