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Princeton Review Mock GMAT Question: Clarification

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Princeton Review Mock GMAT Question: Clarification

by irfanali » Sun Sep 29, 2013 12:41 am
Hello BTG'ites,

Just completed my Mock GMAT and the following are a few questions/clarifications which I seek. Though they seemed straight forward I seemed to have gotten them wrong.

1. On Monday the currency exchange for one yen was 0.008 of a dollar. If on Tuesday, the exchange rate for one yen was 0.007 of a dollar, what was the approximate difference between the 2 rates, expressed in yen per dollar?

a. 0.001
b. 0.01
c. 0.015
d. 1.78
e. 17.8

2. The question has an image, so loading the question screenshot (open as PDF attached)

3. Sue is now 10 years younger than Jane. If in 5 years, Jane will be twice as old as Sue. How old will Sue be in 3 years?
a. 6
b. 8
c. 11
d. 14
e. 18

For my understanding, if you could please explain the steps to arriving at the answer and if there is a shortcut to solving the problem.

Much Appreciated,
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by mevicks » Sun Sep 29, 2013 5:16 am
Hi irfanali,

[spoiler]Are the OAs: E, B, B[/spoiler]

My Reasoning:
irfanali wrote: 1. On Monday the currency exchange for one yen was 0.008 of a dollar. If on Tuesday, the exchange rate for one yen was 0.007 of a dollar, what was the approximate difference between the 2 rates, expressed in yen per dollar?

a. 0.001
b. 0.01
c. 0.015
d. 1.78
e. 17.8
Monday:
1 Y = (8/1000) D
1 D = (1000/8) Yens (Gives the Yen per dollar rate. 1 dollar on the given day would give me these many yens in return)

Tuesday:
1 Y = (7/1000) D
1 D = (1000/7) Yens

Difference:
(1000/7) - (1000/8) = (1000/56)
~ 1000/50
~ 20
Approximate Down the denominator (We can counter this by reducing the division result as the answers are far apart)
Thus the only answer close to 20 is 17.8

2.
Image

In the figure above, triangle RST is equilateral. What is the sum of the lengths of curved lines RS and ST?

(1) Each of the sides of triangle RST is 12.
(2) Curved lines RS and ST are halves of the same circle, and that circle has a diameter of 12.
Rule of thumb : We cant take the geometric figures for granted on the GMAT. We need explicit information to support the figure.

Now, back to the question. We are simply asked to find the lengths of curved lines RS and ST without much information about the type of the two lines. The only information we have is that all the sides of the triangle RST are equal. The curved lines could be a part of a circle or/and an ellipse. Or could be any random curved line. eg:

Image

St1: Gives the value of the sides of RST but we still don't know anything about the two curved lines. INSUFFICIENT
St2: We are given that the lines are the 1/2s of a circle and the equilateral triangle contains these two halves equally. We can find the lengths (2piR) as we know the diameter. SUFFICIENT

[spoiler]Answer: B[/spoiler]

3. Sue is now 10 years younger than Jane. If in 5 years, Jane will be twice as old as Sue. How old will Sue be in 3 years?
a. 6
b. 8
c. 11
d. 14
e. 18


Let the current age of Sue be S
Let the current age of Jane be J

Q: (S + 3) = ?

NOW:
S = J - 10
J = S + 10 ... (i)

IN 5 YEARS:
Sue --> S + 5
Jane --> J + 5
But its given that,
J + 5 = 2(S + 5) ... (ii)

From (i) & (ii)
S + 10 + 5 = 2S + 10
S = 5 (This is the current age)

In 3 Years Sue would be (S + 3) = 5+3 = 8 Years old

Regards,
Vivek
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by Brent@GMATPrepNow » Sun Sep 29, 2013 5:36 am
In the future, please post only one question per thread. Otherwise things can become pretty complicated when there are discussions on multiple questions.

irfanali wrote: 3. Sue is now 10 years younger than Jane. If in 5 years, Jane will be twice as old as Sue. How old will Sue be in 3 years?
a. 6
b. 8
c. 11
d. 14
e. 18
Vivek's solution for the above question is perfect.
I just want to mention that, for these kinds of questions, it's sometimes faster to just check the answer choices. The great thing about this strategy is that it's very easy to do. So, even if you can solve the question algebraically, you might still consider plugging in the answer choices. If you're not 100% sure how to set up the solution algebraically, then you should definitely start plugging in answer choices right away.

Answer choice A: Sue will be 6 in three years.
So, Sue is now 3 years old, which means Jane is now 13 years old
IN FIVE YEARS, Sue will be 8 years old, Jane will be 18 years old.
18 is not twice as old as 8, so answer choice A does not work.

Answer choice B: Sue will be 8 in three years.
So, Sue is now 5 years old, which means Jane is now 15 years old
IN FIVE YEARS, Sue will be 10 years old, Jane will be 20 years old.
20 is twice as old as 10, so answer choice B works.
Done!

Cheers,
Brent
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by irfanali » Mon Sep 30, 2013 5:22 pm
Brent@GMATPrepNow wrote:In the future, please post only one question per thread. Otherwise things can become pretty complicated when there are discussions on multiple questions.

irfanali wrote: 3. Sue is now 10 years younger than Jane. If in 5 years, Jane will be twice as old as Sue. How old will Sue be in 3 years?
a. 6
b. 8
c. 11
d. 14
e. 18
Vivek's solution for the above question is perfect.
I just want to mention that, for these kinds of questions, it's sometimes faster to just check the answer choices. The great thing about this strategy is that it's very easy to do. So, even if you can solve the question algebraically, you might still consider plugging in the answer choices. If you're not 100% sure how to set up the solution algebraically, then you should definitely start plugging in answer choices right away.

Answer choice A: Sue will be 6 in three years.
So, Sue is now 3 years old, which means Jane is now 13 years old
IN FIVE YEARS, Sue will be 8 years old, Jane will be 18 years old.
18 is not twice as old as 8, so answer choice A does not work.

Answer choice B: Sue will be 8 in three years.
So, Sue is now 5 years old, which means Jane is now 15 years old
IN FIVE YEARS, Sue will be 10 years old, Jane will be 20 years old.
20 is twice as old as 10, so answer choice B works.
Done!

Cheers,
Brent
Dear Brent,

But Answer Choice E works as well.

Considering Sue will be 18 in 3 years, viz her age today is 15.

Sue's Age today => S = 15

Therefore Jake's Age today => J = S + 10 => J = 25

Now trying to see if J+5 = 2S => 25 + 5 = 2 (15) => 30 = 30.

Hence, Isn't option E also an answer choice?

Thanks
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by mevicks » Mon Sep 30, 2013 8:37 pm
irfanali wrote:
But Answer Choice E works as well.

...
Your right! But then, it calls the integrity of the mock tests in questions. AFAIK in such cases plugging in numbers should yield only one answer. At least from what ever I've learned about the GMAT in the past few months, GMAT is consistent with this trick. Experts would provide the best explanation for "why E is also correct"!

Regards,
Vivek.
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by umeshpatil » Wed Oct 02, 2013 9:43 am
irfanali wrote: 3. Sue is now 10 years younger than Jane. If in 5 years, Jane will be twice as old as Sue. How old will Sue be in 3 years?
a. 6
b. 8
c. 11
d. 14
e. 18
Dear Brent,

But Answer Choice E works as well.

Considering Sue will be 18 in 3 years, viz her age today is 15.

Sue's Age today => S = 15

Therefore Jake's Age today => J = S + 10 => J = 25

Now trying to see if J+5 = 2S => 25 + 5 = 2 (15) => 30 = 30.

Hence, Isn't option E also an answer choice?

Thanks
No. Question will have unique answer:
You missed to increment age of Sue when you did it for Jane.
If Age(Jane)=25, Age(Sue)=15,
After 5 years, Age(Sue)=20, and Age(Jane)=30.. So, Jane will not be twice as old as Sue. So, (E) is not the answer.
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by irfanali » Wed Oct 02, 2013 11:25 am
Excellent! :)
umeshpatil wrote:
irfanali wrote: 3. Sue is now 10 years younger than Jane. If in 5 years, Jane will be twice as old as Sue. How old will Sue be in 3 years?
a. 6
b. 8
c. 11
d. 14
e. 18
Dear Brent,

But Answer Choice E works as well.

Considering Sue will be 18 in 3 years, viz her age today is 15.

Sue's Age today => S = 15

Therefore Jake's Age today => J = S + 10 => J = 25

Now trying to see if J+5 = 2S => 25 + 5 = 2 (15) => 30 = 30.

Hence, Isn't option E also an answer choice?

Thanks
No. Question will have unique answer:
You missed to increment age of Sue when you did it for Jane.
If Age(Jane)=25, Age(Sue)=15,
After 5 years, Age(Sue)=20, and Age(Jane)=30.. So, Jane will not be twice as old as Sue. So, (E) is not the answer.
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