It is currently 18 Nov 2017, 18:54

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

S99-05

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132619 [0], given: 12326

S99-05 [#permalink]

Show Tags

New post 16 Sep 2014, 01:53
Expert's post
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

59% (01:28) correct 41% (01:34) wrong based on 56 sessions

HideShow timer Statistics

Samantha invests \(i_1\) dollars in bond \(X\), which pays \(r_1\) percent simple interest annually, and she invests \(i_2\) dollars in bond \(Y\), which pays \(r_2\) percent simple interest annually. After one year, will she have earned more interest, in dollars, from bond \(X\) than from bond \(Y\)?


(1) \(r_1^2 \gt r_2^2\)

(2) The ratio of \(i_1\) to \(i_2\) is larger than the ratio of \(r_1\) to \(r_2\).
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132619 [0], given: 12326

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132619 [2], given: 12326

Re S99-05 [#permalink]

Show Tags

New post 16 Sep 2014, 01:53
2
This post received
KUDOS
Expert's post
Official Solution:


The amount of interest, in dollars, that Samantha will receive in one year is equal to the interest rate multiplied by the principal. For bond \(X\), this product is equal to \(\frac{r_1}{100} \times i_1\). Likewise, for bond \(Y\), this product is equal to \(\frac{r_2}{100} \times i_2\).

The question can be rephrased thus: "Is \(\frac{r_1}{100} \times i_1 \gt \frac{r_2}{100} \times i_2\)?" or, after multiplying through by 100, "Is \(r_1i_1 \gt r_2i_2\)?"

Statement 1: INSUFFICIENT. There is no information about \(i_1\) or \(i_2\).

Statement 2: INSUFFICIENT. We can translate this statement to an inequality:
\(\frac{i_1}{i_2} \gt \frac{r_1}{r_2}\)

Since all of the quantities are positive, we can multiply through without worrying about flipping the inequality symbol, and we get the following:
\(i_1r_2 \gt i_2r_1\)

However, we cannot conclude that \(r_1i_1\) is always larger (or always smaller) than \(r_2i_2\). You can choose numbers to see why this is so.

Statements 1 & 2 together: SUFFICIENT. We want to combine the inequalities in such a way as to get \(r_1i_1\) on one side of the inequality symbol and \(r_2i_2\) on the other side -- if possible. In fact, this combination is possible, and the right way to execute it is first to rearrange the second statement in order to put all the same subscripts on one side. We can start from the product we obtained by cross-multiplying:
\(i_1r_2 \gt i_2r_1\)

Now divide each side by both \(r\)'s. Again, since the interest rates are necessarily positive in this scenario (you cannot be paid "negative interest"), we do not have to worry about flipping the sign. We get the following inequality:
\(\frac{i_1}{r_1} \gt \frac{i_2}{r_2}\)

Finally, we multiply this inequality by the inequality from statement 1. (Normally, this is a dangerous move, but once again, since all the quantities are positive, we are allowed to multiply.) Just make sure that the inequality symbols are in the same direction.
\(\frac{i_1}{r_1} \gt \frac{i_2}{r_2}\)
\(r_1^2 \gt r_2^2\)

We wind up with the inequality we're looking for:
\(r_1i_1 \gt r_2i_2\)


Answer: C
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132619 [2], given: 12326

Manager
Manager
avatar
B
Joined: 27 May 2016
Posts: 65

Kudos [?]: 9 [0], given: 0

Location: India
Concentration: Finance, Strategy
GMAT 1: 690 Q49 V34
GPA: 3.2
WE: Engineering (Consulting)
Re: S99-05 [#permalink]

Show Tags

New post 23 Aug 2016, 04:41
I think the correct option should be B. Only statement 2 alone is sufficient to answer the question.

This is how I approached the problem:

Question asks IS r1*i1>r2*i2, which can also be written as (i1/i2)>(r2/r1) (assuming none of the numbers are 0 or negative).

Now Statement 1 is definitely insufficient,
but for Statement 2, it says (i1/i2) > (r1/r2), now this expression also means that (i1/i2) < (r2/r1), which is our desired result. Therefore,sufficient.

Here the assumption is that all the numbers are positive, which is valid as we are comparing investments and interest rates.

Please let me know if I have missed anything in the explanation above.

Thanks!

Kudos [?]: 9 [0], given: 0

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132619 [0], given: 12326

Re: S99-05 [#permalink]

Show Tags

New post 24 Aug 2016, 04:48
jainshubhams92@gmail.com wrote:
I think the correct option should be B. Only statement 2 alone is sufficient to answer the question.

This is how I approached the problem:

Question asks IS r1*i1>r2*i2, which can also be written as (i1/i2)>(r2/r1) (assuming none of the numbers are 0 or negative).

Now Statement 1 is definitely insufficient,
but for Statement 2, it says (i1/i2) > (r1/r2), now this expression also means that (i1/i2) < (r2/r1), which is our desired result. Therefore,sufficient.

Here the assumption is that all the numbers are positive, which is valid as we are comparing investments and interest rates.

Please let me know if I have missed anything in the explanation above.

Thanks!


Please check here: samantha-invests-i1-dollars-in-bond-x-which-pays-r1-102084.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132619 [0], given: 12326

Intern
Intern
avatar
B
Joined: 21 Aug 2017
Posts: 4

Kudos [?]: 0 [0], given: 9

GMAT ToolKit User
Re: S99-05 [#permalink]

Show Tags

New post 06 Sep 2017, 16:17
I have never heard of multiplying an inequality by another inequality ; I didn't think it was even possible.

Kudos [?]: 0 [0], given: 9

Re: S99-05   [#permalink] 06 Sep 2017, 16:17
Display posts from previous: Sort by

S99-05

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: Bunuel, chetan2u



GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.