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13 Sep 2019, 11:39
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
51% (01:43) correct
49%
(01:32)
wrong
based on 490
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Erina has a bag that starts with 50 marbles in it: 10 green marbles and 40 purple marbles. She wants to increase the ratio of green to purple marbles by adding some more marbles to the bag. Which of the following additions would increase this ratio?
I. 3 green and 1 purple
II. 1 green and 3 purple
III. 3 green and 3 purple
A) None would increase the ratio
B) I only
C) I and II only
D) I and III only
E) I, II, and III
I. 3 green and 1 purple
II. 1 green and 3 purple
III. 3 green and 3 purple
A) None would increase the ratio
B) I only
C) I and II only
D) I and III only
E) I, II, and III
13 Sep 2019, 14:13
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Xin Cho
You can approach this one either conceptually, or by actually testing the numbers.
Conceptually, think about what makes a ratio bigger. In math, ratios work the same way as fractions. Suppose that 1/2 of the people in classroom A are wearing glasses. Then, more people join classroom A.
- If exactly half of the new people are wearing glasses, then it will still be the case that exactly 1/2 of the people in the room are wearing glasses.
- But if less than half of the new people are wearing glasses, the fraction of glasses-wearers in classroom A will get smaller, and will now be less than 1/2.
- If more than half of the new people are wearing glasses, the fraction of glasses-wearers in classroom A will get bigger, and will now be more than 1/2.
In general terms, suppose you have things in a ratio of A to B. Then, you add more things, in a ratio of X to Y. If A to B and X to Y are the same ratio - if they're equal - then the ratio you end up with in the end will stay the same. If X to Y is a smaller ratio - that is, if it's more in favor of Y - then the ratio you end up with will also be smaller than the original. And if X to Y is a larger ratio - more in favor of X - the ratio you end up with will be larger than the original.
To solve this problem conceptually, you need to figure out which of the new ratios are smaller or larger than the original one. The original ratio, 10 green to 40 purple, reduces to a ratio of 1 to 4. If we add new marbles in a ratio greater than 1 to 4, the ratio will increase.
And, all three of the new ratios are greater than 1 to 4! Therefore, they'll all cause an increase, and the answer is E.
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Actually testing the numbers is pretty cumbersome and I wouldn't recommend it, but it's worth doing when you review, just to convince yourself.
Original: 10 green, 40 purple.
New I: 13 green, 41 purple. Is 13/41 > 10/40?
Is 13*40 > 10*41?
Is 13*4 > 41?
is 52 > 41? Yes. So, we keep option I.
New II: 11 green, 43 purple. Is 11/43 > 10/40?
Is 11*40 > 10*43?
Is 11*4 > 43?
Is 44>43?
Yes. So, we keep option II.
New III: 13 green, 43 purple. Is 13/43 > 10/40?
Is 13*40 > 43*10?
Is 13*4 > 43?
Is 52 > 43?
Yes. So, we keep option III.
General Discussion
14 Apr 2020, 05:10
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Xin Cho
Solution:
- • \(\frac{(Purple \ Marbles)}{(Green \ Marbles)}= \frac{40}{10}=4\)
Statement I: 3 green and 1 purple
- • \(\frac{(Purple \ Marbles)}{(green \ Marbles)}= \frac{40+1}{10+3} = \frac{41}{ 13 }< 4 \)
- • \(\frac{(Purple \ Marbles)}{(Green \ Marbles)}= \frac{40+3}{10+1} =\frac{43}{ 11} <4 \)
- • \(\frac{(Purple \ Marbles)}{(Green \ Marbles)}= \frac{40+3}{10+3} = \frac{43}{ 13} < 4 \)
