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18 Mar 2024, 08:36
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Records show that over two weeks, everyone who shopped at Best Bet bought one of the cereals, muesli or corn flakes and bought one of the two cereals the folowing week. It was also found that 70 percent of those who bought muesli the first week bought it again the folowing week, and 40 percent of those bought corn flakes the first week bought it again the next week. What percentage of shoppers bought muesli the second week?
(1) The total number of shoppers Best Bet saw in the two weeks was 200,000.
(2) In the first week, 20 percent of shoppers bought muesli.
(1) The total number of shoppers Best Bet saw in the two weeks was 200,000.
(2) In the first week, 20 percent of shoppers bought muesli.
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18 Mar 2024, 14:09
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Gangadhar111990
Records show that over two weeks, everyone who shopped at Best Bet bought one of the cereals, muesli or corn flakes and bought one of the two cereals the folowing week. It was also found that 70 percent of those who bought muesli the first week bought it again the folowing week, and 40 percent of those bought corn flakes the first week bought it again the next week. What percentage of shoppers bought muesli the second week?
(1) The total number of shoppers Best Bet saw in the two weeks was 200,000.
(2) In the first week, 20 percent of shoppers bought muesli.
(1) The total number of shoppers Best Bet saw in the two weeks was 200,000.
(2) In the first week, 20 percent of shoppers bought muesli.
Week 01
- The number of shoppers who bought muesli = x
- The number of shoppers who bought corn flakes= y
- Total shoppers in the first week = x + y
Week 02
- The number of shoppers who bought muesli = 0.7x + 0.6y
- The number of shoppers who bought corn flakes= 0.3y + 0.4y
- Total shoppers in the second week = x + y
Question
\(\frac{0.7x + 0.6y}{2(x+y)}*100\)
Statement 1
(1) The total number of shoppers Best Bet saw in the two weeks was 200,000.
The statement provides us the value of 2(x+y), however, we don't know the value of 0.7x + 0.6y. As the value of the numerator is not known, we cannot find the ratio.
The statement alone is not sufficient. We can eliminate A, and D.
Statement 2
(2) In the first week, 20 percent of shoppers bought muesli.
x = 0.2(x + y)
0.8x = y
\(\frac{0.7x + 0.6y}{2(x+y)}*100\)
Replacing the value of y in the above equation we get
\(\frac{0.7x + 0.6(0.8x)}{2(x+(0.8x))}*100\)
As we have a single variable 'x', the value of 'x' will get canceled out from the numerator and the denominator and we will have a definite value.
We don't have to solve this equation, however, we do have sufficient information to do so.
The statement alone is sufficient.
Option B
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28 Apr 2024, 12:41
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gmatophobia
I could not understand the logic, as in question stem nowhere it is written that shoppers in first week = shoppers in second week. (LMK if we have assumed this)
Week 01
Week 02
Question
\(\frac{0.7x + 0.6y}{2(x+y)}*100\)
Statement 1
(1) The total number of shoppers Best Bet saw in the two weeks was 200,000.
The statement provides us the value of 2(x+y), however, we don't know the value of 0.7x + 0.6y. As the value of the numerator is not known, we cannot find the ratio.
The statement alone is not sufficient. We can eliminate A, and D.
Statement 2
(2) In the first week, 20 percent of shoppers bought muesli.
x = 0.2(x + y)
0.8x = y
\(\frac{0.7x + 0.6y}{2(x+y)}*100\)
Replacing the value of y in the above equation we get
\(\frac{0.7x + 0.6(0.8x)}{2(x+(0.8x))}*100\)
As we have a single variable 'x', the value of 'x' will get canceled out from the numerator and the denominator and we will have a definite value.
We don't have to solve this equation, however, we do have sufficient information to do so.
The statement alone is sufficient.
Option B
I could not understand the logic, as in question stem nowhere it is written that shoppers in first week = shoppers in second week. (LMK if we have assumed this)
gmatophobia
Gangadhar111990
Records show that over two weeks, everyone who shopped at Best Bet bought one of the cereals, muesli or corn flakes and bought one of the two cereals the folowing week. It was also found that 70 percent of those who bought muesli the first week bought it again the folowing week, and 40 percent of those bought corn flakes the first week bought it again the next week. What percentage of shoppers bought muesli the second week?
(1) The total number of shoppers Best Bet saw in the two weeks was 200,000.
(2) In the first week, 20 percent of shoppers bought muesli.
(1) The total number of shoppers Best Bet saw in the two weeks was 200,000.
(2) In the first week, 20 percent of shoppers bought muesli.
Week 01
- The number of shoppers who bought muesli = x
- The number of shoppers who bought corn flakes= y
- Total shoppers in the first week = x + y
Week 02
- The number of shoppers who bought muesli = 0.7x + 0.6y
- The number of shoppers who bought corn flakes= 0.3y + 0.4y
- Total shoppers in the second week = x + y
Question
\(\frac{0.7x + 0.6y}{2(x+y)}*100\)
Statement 1
(1) The total number of shoppers Best Bet saw in the two weeks was 200,000.
The statement provides us the value of 2(x+y), however, we don't know the value of 0.7x + 0.6y. As the value of the numerator is not known, we cannot find the ratio.
The statement alone is not sufficient. We can eliminate A, and D.
Statement 2
(2) In the first week, 20 percent of shoppers bought muesli.
x = 0.2(x + y)
0.8x = y
\(\frac{0.7x + 0.6y}{2(x+y)}*100\)
Replacing the value of y in the above equation we get
\(\frac{0.7x + 0.6(0.8x)}{2(x+(0.8x))}*100\)
As we have a single variable 'x', the value of 'x' will get canceled out from the numerator and the denominator and we will have a definite value.
We don't have to solve this equation, however, we do have sufficient information to do so.
The statement alone is sufficient.
Option B
