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09 Sep 2024, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
50% (02:27) correct
50%
(02:29)
wrong
based on 185
sessions
History
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Not Attempted Yet
The inventory of grape jelly on a store's shelves consists only of 2-ounce, 6-ounce, and 16-ounce jars. If the average jar size of the current inventory is 6.4 ounces, how many additional 2-ounce jars must be put on the shelves to reduce the average size to 6.0 ounces?
(1) The current ratio of 2-ounce to 6-ounce to 16-ounce jars is 15:27:8.
(2) There are initially 7 more 2-ounce jars than 16-ounce jars.
(1) The current ratio of 2-ounce to 6-ounce to 16-ounce jars is 15:27:8.
(2) There are initially 7 more 2-ounce jars than 16-ounce jars.
The inventory of grape jelly on a store's shelves consists only of 2-ounce, 6-ounce, and 16-ounce jars. If the average jar size of the current inventory is 6.4 ounces, how many additional 2-ounce jars must be put on the shelves to reduce the average size to 6.0 ounces?
(1) The current ratio of 2-ounce to 6-ounce to 16-ounce jars is 15:27:8.
Theres is a relation between the three so we can find the common factor x in all of them as in if 15x, 27x and 8x are number of jars of 2-ounce, 6-ounce and 16-ounce jars respectively. Hence we can find the value of more 2-ounce that needs to be added by keeping other ones same so that avergae comes down to 6.
\(\frac{(15x * 2 + 27x*6 + 8x*16) }{ (15x + 27x + 8x)}\) = 6.4
But x takes any value greater than equal to 1 i.e. x = 1 or 2 or 3 ... all satisfy which is not possible
INSUFFICIENT.
(2) There are initially 7 more 2-ounce jars than 16-ounce jars.
Here's a catch. We may initially choose to eliminate this but this statement creates a boundation that eventually creates a mirage that it can give us the answer.
Taking a clue from the Statement 1, we see that the number of 2-ounce and 16-ounce jars can be 15 and 8(other false possibilities that we may think are 7 and 0 or 8 and 1 or 9 and 2 and so on.. ), however, other possibilities(except those that are mulitples of 15 and 8) would lead to non-integer value of 6-ounce jars which is not possible. This is because 6-ounce jars too would have to be considered which has to be in specific ratio(let is be anything) with both 2-ounce and 16-ounce jars. But the relation of 6-ounce jars to the other two is not given and neither can be found based on the imputs available.
INSUFFICIENT.
Together 1 and 2
To understand better, think of the ratio of sumproduct(number of jars and weight of each type of jars) and total number of jars being in the ratio 64/10. Here, number of jars is in the multiple of 10(10,20, 30, 40, ....) and we need to fine balance it so that in that ratio sumproduct is a multiple of 64.
If one brainstorms more it can be found that the minimum number of jars that satisfy the condition is 50(the clue from Statement 1 helps). Next then is 100 but it disregards the condition of 2-ounce jars being 7 more than 16-ounce bars.
SUFFICIENT.
HTHs.
Answer C.
(1) The current ratio of 2-ounce to 6-ounce to 16-ounce jars is 15:27:8.
Theres is a relation between the three so we can find the common factor x in all of them as in if 15x, 27x and 8x are number of jars of 2-ounce, 6-ounce and 16-ounce jars respectively. Hence we can find the value of more 2-ounce that needs to be added by keeping other ones same so that avergae comes down to 6.
\(\frac{(15x * 2 + 27x*6 + 8x*16) }{ (15x + 27x + 8x)}\) = 6.4
But x takes any value greater than equal to 1 i.e. x = 1 or 2 or 3 ... all satisfy which is not possible
INSUFFICIENT.
(2) There are initially 7 more 2-ounce jars than 16-ounce jars.
Here's a catch. We may initially choose to eliminate this but this statement creates a boundation that eventually creates a mirage that it can give us the answer.
Taking a clue from the Statement 1, we see that the number of 2-ounce and 16-ounce jars can be 15 and 8(other false possibilities that we may think are 7 and 0 or 8 and 1 or 9 and 2 and so on.. ), however, other possibilities(except those that are mulitples of 15 and 8) would lead to non-integer value of 6-ounce jars which is not possible. This is because 6-ounce jars too would have to be considered which has to be in specific ratio(let is be anything) with both 2-ounce and 16-ounce jars. But the relation of 6-ounce jars to the other two is not given and neither can be found based on the imputs available.
INSUFFICIENT.
Together 1 and 2
To understand better, think of the ratio of sumproduct(number of jars and weight of each type of jars) and total number of jars being in the ratio 64/10. Here, number of jars is in the multiple of 10(10,20, 30, 40, ....) and we need to fine balance it so that in that ratio sumproduct is a multiple of 64.
If one brainstorms more it can be found that the minimum number of jars that satisfy the condition is 50(the clue from Statement 1 helps). Next then is 100 but it disregards the condition of 2-ounce jars being 7 more than 16-ounce bars.
SUFFICIENT.
HTHs.
Answer C.
09 Sep 2024, 07:39
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unraveled
According to me,
The equation you mentioned (\(\frac{(15x * 2 + 27x*6 + 8x*16) }{ (15x + 27x + 8x)}\) = 6.4) can not be solved, as x will cancel out itself from the numerator and the denominator.
So, St.1 alone is not sufficient. Hence Eleminating A & D.
For St.2,
To justify St.2, we CANNOT take any clues from st.1, and as st.2 in this case alone is not sufficient, we can eliminate it.
Hence, eliminating B.
Of course, now if we consider both statements together, we can easily get the value of x and hence the required answer.
So the correct answer choice will be C.
Correct me if required. Thanks.
