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05 Jun 2024, 01:30
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Difficulty:
35%
(medium)
Question Stats:
72% (01:53) correct
28%
(01:57)
wrong
based on 103
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Jamie purchased three items from a budget store. She received discounts of 40% on the marked price of item A, 20% on the marked price of item B and 10% on the marked price of item C. How much money did she save, in percent terms, by shopping at the budget store?
(1) The marked price of item B is 75% of the marked price of item A and 200% more than the marked price of item C.
(2) The marked price of item A is 400% of the marked price of item C.
(1) The marked price of item B is 75% of the marked price of item A and 200% more than the marked price of item C.
(2) The marked price of item A is 400% of the marked price of item C.
05 Jun 2024, 05:09
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Bunuel
I think A,
Given - Jamie purchased three items from a budget store. She received discounts of 40% on the marked price of item A, 20% on the marked price of item B and 10% on the marked price of item C.
Lets assume marked price of A = 100x, B = 100y and C = 100z.
Discount offered A = 40x, B = 20x and C = 10x.
lets calculate, How much money did she save, in percent terms, by shopping at the budget store based on given below conditions.
1st - The marked price of item B is 75% of the marked price of item A and 200% more than the marked price of item C.
Therefore 100y = 75x = 300z.
from there we will get 4y = 3x = 12z = k (constant)
from there get the values in terms of x, y and z.
they will be x = k/3, y = k/4 and z = k/12.
from here you can calculate total amount and total discount values in terms of k and after that we can get the value in percentage for how much money did she save. Hence Sufficient.
2nd - The marked price of item A is 400% of the marked price of item C.
Therefore 100x = 400z which is x=4z. but there is nothing about marked price of B given so not sufficient.
Hence A.
05 Jun 2024, 05:57
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Original prices: \(a\), \(b \) & \(c\)
Discounted prices: \(\frac{6}{10}a\), \(\frac{8}{10}b\) & \(\frac{9}{10}c\)
In terms of percent, the amount saved will will be the sum of one minus the fraction of each of the discounted prices over the sum of the original prices multiplied by 100 ie. \(\frac{\frac{4}{10}a+\frac{2}{10}b+\frac{1}{10}c}{a+b+c}*100\)
If one can represent each of the algebraic values of a, b & c in terms of single algebraic then one will be able to answer the question.
(1) The marked price of item B is 75% of the marked price of item A and 200% more than the marked price of item C.
From the statement one can gets that:
\(b = \frac{3}{4}a\), in terms of a: \(\frac{4}{3}b = a\)
and that \(b = 3c\), in terms of c: \(\frac{1}{3}b = c\)
In terms of b, the three respective original prices are: \(\frac{4}{3}b\), \(b\) & \(\frac{1}{3}b\). This is enough to be able to answer the question.
SUFFICIENT
MATHS: \(\frac{(\frac{4}{10}*\frac{4}{3}b)+(\frac{2}{10}b)+(\frac{1}{10}*\frac{1}{3}b)}{\frac{4}{3}b+b+\frac{1}{3}b}*100\)
\(\frac{\frac{8}{15}b + \frac{2}{10}b +\frac{1}{30}b}{\frac{8}{3}b}*100\)
\(\frac{16+6+1}{30}b * \frac{3}{8} * 100\)
\(\frac{23}{2}b * \frac{1}{2}b * 5\)
\(\frac{115}{4}\)
\(28.75\)%
(2) The marked price of item A is 400% of the marked price of item C.
This gives us \(a = 4c\), however, without knowing the value of b in terms of a or c it is impossible to solve the percent saved.
INSUFFICIENT
ANSWER A
Discounted prices: \(\frac{6}{10}a\), \(\frac{8}{10}b\) & \(\frac{9}{10}c\)
In terms of percent, the amount saved will will be the sum of one minus the fraction of each of the discounted prices over the sum of the original prices multiplied by 100 ie. \(\frac{\frac{4}{10}a+\frac{2}{10}b+\frac{1}{10}c}{a+b+c}*100\)
If one can represent each of the algebraic values of a, b & c in terms of single algebraic then one will be able to answer the question.
(1) The marked price of item B is 75% of the marked price of item A and 200% more than the marked price of item C.
From the statement one can gets that:
\(b = \frac{3}{4}a\), in terms of a: \(\frac{4}{3}b = a\)
and that \(b = 3c\), in terms of c: \(\frac{1}{3}b = c\)
In terms of b, the three respective original prices are: \(\frac{4}{3}b\), \(b\) & \(\frac{1}{3}b\). This is enough to be able to answer the question.
SUFFICIENT
MATHS: \(\frac{(\frac{4}{10}*\frac{4}{3}b)+(\frac{2}{10}b)+(\frac{1}{10}*\frac{1}{3}b)}{\frac{4}{3}b+b+\frac{1}{3}b}*100\)
\(\frac{\frac{8}{15}b + \frac{2}{10}b +\frac{1}{30}b}{\frac{8}{3}b}*100\)
\(\frac{16+6+1}{30}b * \frac{3}{8} * 100\)
\(\frac{23}{2}b * \frac{1}{2}b * 5\)
\(\frac{115}{4}\)
\(28.75\)%
(2) The marked price of item A is 400% of the marked price of item C.
This gives us \(a = 4c\), however, without knowing the value of b in terms of a or c it is impossible to solve the percent saved.
INSUFFICIENT
ANSWER A
