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Annie multiplied the date of her birthday by 5, then subtrac

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by Max@Math Revolution » Mon Dec 30, 2019 12:11 am
[GMAT math practice question]

Annie multiplied the date of her birthday by 5, then subtracted 4 from that. She multiplied it by 2 after that and added the month of her birthday again. She got the result of 232. When is her birthday?

A. Aug. 20th
B. Aug. 23rd
C. Sep. 21st
D. Sep. 22nd
E. Oct. 23rd
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by SampathKp » Mon Dec 30, 2019 2:42 am
Max@Math Revolution wrote:[GMAT math practice question]

Annie multiplied the date of her birthday by 5, then subtracted 4 from that. She multiplied it by 2 after that and added the month of her birthday again. She got the result of 232. When is her birthday?

A. Aug. 20th
B. Aug. 23rd
C. Sep. 21st
D. Sep. 22nd
E. Oct. 23rd
Let the date of Annie birthday be X
(5x-4) 2+30 = 232
X= 21

Answer is C
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by Max@Math Revolution » Wed Jan 01, 2020 2:10 am
=>

Assume m and d are the month and date of Annie's birthday.
Then we have 2(5d - 4) + m = 232 or m = 240 - 10d = 10(24-d).
Since m is a multiple of 10, we have m = 10. (Note that m cannot be 20, 30, etc. because there are only 12 months in a year.)
Then we have 10d = 240 - m, 10d = 240 - 10, 10d = 230 or d = 23.

Thus, Annie's birthday is Oct. 23rd.

Therefore, E is the answer.
Answer: E
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