Over a certain time period, did the number of shares of stock in Ruth's portfolio increase?

1) Over the time period, the ratio of the number of shares of stock to the total number of shares of stocks and bonds in Ruth's portfolio increased.
2) Over the time period, the total number of shares of stock and bonds in Ruth's portfolio increased

A
B
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D
E

Qs: Can you use the BD ACE grid, the rephrasing technique (and/or VIC) to show me how to solve this problem? Also, if you can reveal any underlying concept in ratios that this DS question is testing, it will be helpful? What is the typical range of this question?

Thank you

This is definitely a 700+ question.

There is not a particularly useful rephrase of this question, although it would help to assign some variables. I think it makes sense to preview the statements; at least they tell us what variables we will need to define. So, if we call S the number of shares of stock and B the number of shares of bonds, the problem really is:

“Did S increase?”
(1) S/(S + B) increased.
(2) S + B increased.

Statement (1) is testing a ratio or fraction property: what happens as we vary the numerator and the denominator relative to each other? what are the ways a fraction would increase?

There are several approaches that would work:
a) List all 9 (=3^2) of the increase/decrease/no change scenarios for the variables S and B in a chart, then use the statements to include or exclude the scenarios.
b) Use the statements to list increase/decrease/no change possibilities for S.
c) Try numbers.
d) Some combination of the above.

Statement (2) is easier, so using the BD/ACE grid makes sense.

(2) INSUFFICIENT:
S + B could increase a number of ways:
S increase, B increase,
S no change, B increase,
S decrease, B increase (more so),
etc.
Probably no need to pick numbers here, although you could if you wanted to verify.

(1) INSUFFICIENT: The best way to interpret this ratio is to rely on fraction property rules to simplify. Note that S and B are non-negative. If the positive value X increases, then 1/X decreases. So if S/(S + B) increased, then (S + B)/S decreased. (S + B)/S = 1 + B/S, so we can conclude that B/S decreased.

B/S could decrease a number of ways:
S increase, B decrease,
S no change, B decrease,
S decrease, B decrease (more so),
etc.

But, I have to admit that I might just pick some numbers to see what could happen.

Let’s say that S = 10 and B = 20 at the beginning, so our original S/(S + B) = 10/(10 + 20) = 10/30 = 1/3. It’s best to try to prove insufficiency, which means we should try to make this ratio increase by both increasing S and not increasing S.

The ratio could increase if we increase S:
S increases to 12, B stays at 20, so the new S/(S + B) = 12/(12 + 20) = 12/32 > 1/3.

The ratio could increase if we don’t increase S:
S stays at 10, B decreases to 2, so the new S/(S + B) = 10/(10 + 2) = 10/12 = 5/6 > 1/3.

S could either increase or not.

(1) and (2) SUFFICIENT: Note that in order for the fraction S/(S + B) to increase as its denominator (S + B) increased, the numerator S must have increased, too.

_________________
Emily Sledge
Instructor
ManhattanGMAT

This is a great question and one that I would get wrong almost 100% of the time unless I practiced "thinking" this way.

I think that once you figure out what the question is asking, you don't have to do all the algebra- just think something like:

"If both the numerator AND denominator increase, the numerator has to increase even more than the denominator or else the entire value would decrease."

For me, the tricky part was the following:

Question: "Over a certain time period, did the number of shares of stock in Ruth's portfolio increase? "

Part B: "
2) Over the time period, the total number of shares of stock and bonds in Ruth's portfolio increased"

I read part B as Stocks increased and bonds increased, not that the "entire denominator" increased.

To me, saying A and B increased means:

A increased AND B increased
Not
quantity (A+B) increased

What am I missing grammatically or logically here? I have a feeling the GMAT tests these concepts a lot at the 700+ level and unless I recognize my nuancical mistake, I will be addled every time I'm tested on this. I found a DS problem in OG 12 talking about "price and tax" that seems to test the same concept of being able to read the question rather than perform the math of answering it. I was torched by that question as well. Eventually, I got it I had that "DUH" moment where I was mad for not "seeing" what the question was actually asking and for taking the "easy" bait. Unfortunately, that moment came after a few hours and a post on another board, pleading for help.

Can anyone offer a hint here. Thank you.

i feel your pain on the interpretation part.



there are definitely problems that are difficult to interpret. in fact, there are a couple that are genuinely ambiguous, requiring you to rely on "convention" to interpret them correctly. i can post an example or two of those, if you'd like, on this thread. just reply and let me know.

this problem, though, is not one of those. there are two clear indicators that we're talking about an increase in S + B, and not about separate increases in the two quantities; one of those indicators is very plain, while the other is somewhat subtle.

here you go:



the blue word "TOTAL" should tell you at once that you're talking about ... a total. not two separate components.

the purple word is more subtle, but it communicates the same fact: it uses the singular term "number". if we were talking about two separate increases in two separate quantities, the word would have to be plural "numbers".

Just for clarity: The above statement COULD suggest that in s/(s+b) . the numerator s must increase more than that the denominator (s+b) and therefore (i) is sufficient as it states that the ratio of s to (s+b) increased? What am missing?

thx.

You are quoting something that another student wrote, so we need to evaluate whether what the student said is correct.

I can show a case in which this is not true. For example, let's assume that your original expression is 1/2. Obviously the numerator is 1 and the denominator is 2.

If I add 1 to the numerator and 2 to the denominator, the new expression is 2/4, which is the same as 1/2. In this case the denominator increased by more than the numerator but the expression stayed the same; it did not decrease.

I would recommend that you stick with Emily and Ron's postings in resolving this problem. Thanks!

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Jamie Nelson
ManhattanGMAT Instructor