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07 Jun 2022, 05:30
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In Ghazal’s doll collection, (3/5)th of the dolls are Barbie dolls, and (4/7)th of the Barbies were purchased before the age of 10. If 90 dolls in Ghazal’s collection are Barbies that were purchased at the age of 10 or later, how many dolls in her collection are non-Barbie dolls?
(A) 70
(B) 90
(C) 140
(D) 154
(E) 192
(A) 70
(B) 90
(C) 140
(D) 154
(E) 192
genericUser
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07 Jun 2022, 08:52
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In Ghazal’s doll collection, (3/5)th of the dolls are Barbie dolls, and (4/7)th of the Barbies were purchased before the age of 10. If 90 dolls in Ghazal’s collection are Barbies that were purchased at the age of 10 or later, how many dolls in her collection are non-Barbie dolls?
with reference to the figure, we wnow that 90 is the 3/5 (Barbie among all kind of dolls) of 3/7 (dools purchased at age greater or equal to 10); we can therfore workout such equation
\(90=\frac{3}{5}*\frac{3}{7}*t\)
from which we get \(t=350\)
then we need to to get the non-Barbie dools, and so the \(1-\frac{3}{5}=\frac{2}{5}\) of the total
\(nB=350*\frac{2}{5}=140\)
(A) 70
(B) 90
(C) 140
(D) 154
(E) 192
feedback appreciated
with reference to the figure, we wnow that 90 is the 3/5 (Barbie among all kind of dolls) of 3/7 (dools purchased at age greater or equal to 10); we can therfore workout such equation
\(90=\frac{3}{5}*\frac{3}{7}*t\)
from which we get \(t=350\)
then we need to to get the non-Barbie dools, and so the \(1-\frac{3}{5}=\frac{2}{5}\) of the total
\(nB=350*\frac{2}{5}=140\)
(A) 70
(B) 90
(C) 140
(D) 154
(E) 192
feedback appreciated
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tab.png [ 4.99 KiB | Viewed 2634 times ]
07 Jun 2022, 11:22
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The dolls in Ghazal’s collection are Barbie dolls or they are not; similarly, the dolls were purchased before the age of 10 or at an age of 10 or later.
Observe that the data here is mutually exclusive – meaning there can be no overlap or common region. Therefore, drawing a 2 x 2 grid is the easiest way to solve this question.
Since we see a 5 and a 7 in the denominators of the fractions, let the total number of dolls in her collection be 35x. Applying the constraints given in the question, the grid can be filled up as shown below:
07th June 2022 - Post 4.png [ 11.95 KiB | Viewed 2576 times ]
Now, the Barbie dolls in Ghazal’s collection, which were purchased at an age of 10 years or later is given as 90; from the table, we see that it is 9x.
Therefore, 9x = 90 or x = 10.
We need to find out the number of non-barbie dolls in Ghazal’s collection; from the table, clearly, that is a total of 14x.
Therefore, number of non-Barbie dolls in her collection = 14 * 10 = 140.
The correct answer option is C.
Observe that the data here is mutually exclusive – meaning there can be no overlap or common region. Therefore, drawing a 2 x 2 grid is the easiest way to solve this question.
Since we see a 5 and a 7 in the denominators of the fractions, let the total number of dolls in her collection be 35x. Applying the constraints given in the question, the grid can be filled up as shown below:
Attachment:
07th June 2022 - Post 4.png [ 11.95 KiB | Viewed 2576 times ]
Now, the Barbie dolls in Ghazal’s collection, which were purchased at an age of 10 years or later is given as 90; from the table, we see that it is 9x.
Therefore, 9x = 90 or x = 10.
We need to find out the number of non-barbie dolls in Ghazal’s collection; from the table, clearly, that is a total of 14x.
Therefore, number of non-Barbie dolls in her collection = 14 * 10 = 140.
The correct answer option is C.
