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29 Apr 2022, 01:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
70% (02:18) correct
30%
(02:30)
wrong
based on 211
sessions
History
Date
Time
Result
Not Attempted Yet
A certain energy bar can be purchased individually for $1.50; a package of three of the same bars sells for $4.00. During halftime at a sports event, a nonprofit organization sold 750 energy bars as a fund-raiser. What is the dollar amount of these energy bar sales?
(1) If all the energy bars had been sold individually, the nonprofit would have earned $75 more than it did.
(2) The sales revenue from individual bars was 25 percent less than the sales revenue from the three-packs.
(1) If all the energy bars had been sold individually, the nonprofit would have earned $75 more than it did.
(2) The sales revenue from individual bars was 25 percent less than the sales revenue from the three-packs.
29 Apr 2022, 11:02
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Step 1: Analyse Question Stem
An energy bar can be purchased individually or in packs of 3.
When purchased individually, each bar costs $1.50
When purchased in a pack of 3, it costs $4 to buy the pack. Therefore, effective cost of 1 bar = $ \(\frac{4}{3}\).
A total of 750 bars were sold during a fund-raiser.
We have to find the dollar amount from the sales of these bars at the fund-raiser. To find the total revenue, we need the individual values of how many bars were sold individually and how many were sold as packs.
Let the number of energy bars that were sold individually be x. Let the number of energy bars sold as a pack be y.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: If all the energy bars had been sold individually, the non-profit would have earned $75 more than it did.
If all the 750 bars had been sold individually, revenue = 750 * 1.50 = 750 * \(\frac{3 }{ 2} \)= 375 * 3 = $1125.
Now, as per statement 1, this is $75 more than what the non-profit actually earned, i.e.,
1125 = Actual revenue earned by non-profit + 75.
Therefore, actual revenue earned by non-profit = 1125 – 75 = 1050.
The data in statement 1 is sufficient to find out the dollar amount from the sales of the 750 energy bars at the fund raiser.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: The sales revenue from individual bars was 25 percent less than the sales revenue from the three-packs.
Sales revenue from individual bars = x * \(\frac{3}{2}\) = \(\frac{3x }{ 2}\)
Sales revenue from the packs = y * \(\frac{4}{3}\) = \(\frac{4y }{ 3}\)
Therefore, \(\frac{3x }{ 2}\) = 75 percent of \(\frac{ 4y }{ 3}\)
\(\frac{3x }{ 2}\) = \(\frac{3 }{ 4}\) * \(\frac{4y }{ 3}\)
Simplifying, we have,
\(\frac{x }{ y} \)= \(\frac{2 }{ 3}\).
From this information, we can only find the number of chocolates that were sold individually and those that were sold as packs.
Since statement 2 does not provide any data about the prices at which they were sold, the dollar amount of the total sales cannot be calculated.
The data in statement 2 is insufficient to find out the dollar amount from the sale of the 750 energy bars at the fund raiser.
Statement 2 alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.
An energy bar can be purchased individually or in packs of 3.
When purchased individually, each bar costs $1.50
When purchased in a pack of 3, it costs $4 to buy the pack. Therefore, effective cost of 1 bar = $ \(\frac{4}{3}\).
A total of 750 bars were sold during a fund-raiser.
We have to find the dollar amount from the sales of these bars at the fund-raiser. To find the total revenue, we need the individual values of how many bars were sold individually and how many were sold as packs.
Let the number of energy bars that were sold individually be x. Let the number of energy bars sold as a pack be y.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: If all the energy bars had been sold individually, the non-profit would have earned $75 more than it did.
If all the 750 bars had been sold individually, revenue = 750 * 1.50 = 750 * \(\frac{3 }{ 2} \)= 375 * 3 = $1125.
Now, as per statement 1, this is $75 more than what the non-profit actually earned, i.e.,
1125 = Actual revenue earned by non-profit + 75.
Therefore, actual revenue earned by non-profit = 1125 – 75 = 1050.
The data in statement 1 is sufficient to find out the dollar amount from the sales of the 750 energy bars at the fund raiser.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: The sales revenue from individual bars was 25 percent less than the sales revenue from the three-packs.
Sales revenue from individual bars = x * \(\frac{3}{2}\) = \(\frac{3x }{ 2}\)
Sales revenue from the packs = y * \(\frac{4}{3}\) = \(\frac{4y }{ 3}\)
Therefore, \(\frac{3x }{ 2}\) = 75 percent of \(\frac{ 4y }{ 3}\)
\(\frac{3x }{ 2}\) = \(\frac{3 }{ 4}\) * \(\frac{4y }{ 3}\)
Simplifying, we have,
\(\frac{x }{ y} \)= \(\frac{2 }{ 3}\).
From this information, we can only find the number of chocolates that were sold individually and those that were sold as packs.
Since statement 2 does not provide any data about the prices at which they were sold, the dollar amount of the total sales cannot be calculated.
The data in statement 2 is insufficient to find out the dollar amount from the sale of the 750 energy bars at the fund raiser.
Statement 2 alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.
29 Apr 2022, 19:25
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Let x be the number of individually sold energy bar
Let y be the number of 3-unit packages
We have
x + 3y = 750 (1)
(1) Only
1.5x + 4y + 75 = 1.5*750 (2)
We should be able to solve the system of equations comprising (1) and (2).
Sufficient
(The solution is y = 150 and x = 300. But we definitely do not want to do the actual calculation in the test center.)
(2) Only
1.50x = (3/4)*4y
=> x = 2y (3)
We should be able to solve the system of equations comprising (1) and (3).
Sufficient
The answer is thus (D).
Let y be the number of 3-unit packages
We have
x + 3y = 750 (1)
(1) Only
1.5x + 4y + 75 = 1.5*750 (2)
We should be able to solve the system of equations comprising (1) and (2).
Sufficient
(The solution is y = 150 and x = 300. But we definitely do not want to do the actual calculation in the test center.)
(2) Only
1.50x = (3/4)*4y
=> x = 2y (3)
We should be able to solve the system of equations comprising (1) and (3).
Sufficient
The answer is thus (D).
