Three Lottery Winners- X, Y, and Z- are Sharing A Lottery Jackpot GMAT Problem Solving

Question: Three lottery winners- X, Y, and Z- are sharing a lottery jackpot. X’s share is\(1\over5\)of Y’s share and\(1\over7\)of Z’s share. If the total jackpot is $195,000, what is the dollar amount of Z’s share?

1. $15,000
2. $35,000
3. $75,000
4. $105,000
5. $115,000

Answer:
Approach Solution (1):
We can write every other variable in terms of Z. X’s share is\(Z\over7\).\(1\over5\)of Y’s share is equal to\(1\over7\)of Z’s share, so we have\(Y={5\over7}Z\)
Then X + Y + Z =\({1\over7}Z+{5\over7}Z+Z={13\over7}Z=195,000\)
\(Z={195,000\over13}*7=15,00*7=105,000\)
Correct option: D

Approach Solution (2):
\(x ---(1)\)
\(x = {({1\over5})}y\therefore{y=5x}---(2)\)
\(x = {({1\over7})}z\therefore{z=7x}---(3)\)
\(\therefore{x+y+z=195,000}\)
\(\therefore{x+5x+7x=195,000}\)
\(13x=195,000\)
\(x=15,000\)
\(y=5x=75,000\)
\(z=7x=105,000\)
Correct option: D

Approach Solution (3):
After understanding the question and reading the values, we will get:
X + Y + Z =\({1\over7}Z+{5\over7}Z+Z={13\over7}Z=195,000\)
\(Z={195,000\over13}*7=15,00*7=105,000\)
Correct option: D

“Three lottery winners- X, Y, and Z- are sharing a lottery jackpot. X’s share is\(1\over5\)of Y’s share and\(1\over7\)of Z’s share. If the total jackpot is $195,000, what is the dollar amount of Z’s share?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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