Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 08 Nov 2009
Posts: 15

Samantha invests i1 dollars in bond X, which pays r1
[#permalink]
Show Tags
Updated on: 02 Oct 2010, 13:41
Question Stats:
59% (01:27) correct 41% (01:17) wrong based on 227 sessions
HideShow timer Statistics
Samantha invests i1 dollars in bond X, which pays r1 percent simple interest annually, and she invests i2 dollars in bond Y, which pays r2 percent simple interest annually. After one year, will she have earned more interest, in dollars, from bond X than from bond Y ? (1) \((r1)^2 > (r2)^2\) (2) The ratio of i1 to i2 is larger than the ratio of r1 to r2 . Why cant 1 be sufficient . We know that interest cannot be negative , therefore (1) eventually leads to r1> r2 . The values of i1 and I2 don’t matter , because even when i2 is greater than i1 , the interest would be less .Eg. i1 : 100 r1: 5% , i2: 150 , r2: 3% , i1r1 > i2r2 giving the required result .
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by nandini11 on 02 Oct 2010, 11:56.
Last edited by nandini11 on 02 Oct 2010, 13:41, edited 1 time in total.



Retired Moderator
Joined: 02 Sep 2010
Posts: 774
Location: London

Re: GMAT Club Test MGMAT Challenge Test 1 DS Question(#5)
[#permalink]
Show Tags
02 Oct 2010, 12:33
nandini11 wrote: Samantha invests i1 dollars in bond X , which pays r1 percent simple interest annually, and she invests i2 dollars in bond Y , which pays r2 percent simple interest annually. After one year, will she have earned more interest, in dollars, from bond X than from bond Y ? 1. \((r1)^2 > (r2)^2\) 2. The ratio of i1 to i2 is larger than the ratio of r1 to r2 .
Why cant 1 be sufficient . We know that interest cannot be negative , therefore (1) eventually leads to r1> r2 . The values of i1 and I2 don’t matter , because even when i2 is greater than i1 , the interest would be less .Eg. i1 : 100 r1: 5% , i2: 150 , r2: 3% , i1r1 > i2r2 giving the required result .
OA Interest from bond X : i1*r1/100 Interest from bond Y : i2*r2/100 we need to know if i1*r1 > i2*r2 ? (1) r1^2 > r2^2 ... Not sufficient as it doesn't tell us anything about the actual amounts invested (2) i1/i2 > r1/r2 which implies i1*r2 > i2*r1 ... doesnt help us solve our inequality (1+2) r1^2 > r2^2 So r1 > r2 as interest rate on bond cannot be negative i1*r1 > i1*r2 i2*r1 > i2*r2 Combining with condition known from Statement 2, we get i1*r1 > i2*r2 Answer is (C)sibanmishra wrote: Well..i think the answer is E. Because in bonds the interest can be ve and a variable one. Bonds can't have negative interest. Variable is irrelevant here as we are given it is fixed
_________________
Math writeups 1) Algebra101 2) Sequences 3) Set combinatorics 4) 3D geometry
My GMAT story
GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Sep 2009
Posts: 47977

Re: GMAT Club Test MGMAT Challenge Test 1 DS Question(#5)
[#permalink]
Show Tags
02 Oct 2010, 13:24
nandini11 wrote: Samantha invests i1 dollars in bond X , which pays r1 percent simple interest annually, and she invests i2 dollars in bond Y , which pays r2 percent simple interest annually. After one year, will she have earned more interest, in dollars, from bond X than from bond Y ? 1. \((r1)^2 > (r2)^2\) 2. The ratio of i1 to i2 is larger than the ratio of r1 to r2 .
Why cant 1 be sufficient . We know that interest cannot be negative , therefore (1) eventually leads to r1> r2 . The values of i1 and I2 don’t matter , because even when i2 is greater than i1 , the interest would be less .Eg. i1 : 100 r1: 5% , i2: 150 , r2: 3% , i1r1 > i2r2 giving the required result .
OA First of all: "bond X pays r1 percent simple interest annually" > so r1 and r2 can not be negative. After 1 year bond X will earn \(i_1*\frac{r_1}{100}\) and bond Y \(i_2*\frac{r_2}{100}\). So the question is \(i_1*\frac{r_1}{100}>i_2*\frac{r_2}{100}\)? > is \(i_1*r_1>i_2*r_2\)? (1) \((r_1)^2>(r_2)^2\) > not sufficient as no info about \(i_1\) and \(i_2\). (2) The ratio of i1 to i2 is larger than the ratio of r1 to r2 > \(\frac{i_1}{i_2}>\frac{r_1}{r_2}\) > \(i_1*r_2>i_2*r_1\). Not sufficient. (1)+(2) From (1) \((r_1)^2>(r_2)^2\) > \(r_1>r_2\) > \(\frac{r_1}{r_2}>1\) > so \(\frac{i_1}{i_2}>\frac{r_1}{r_2}>1\) > \(\frac{i_1}{i_2}>1\) > \(i_1>i_2\). So as both \(r_1>r_2\) and \(i_1>i_2\) then \(i_1*r_1>i_2*r_2\). Sufficient. Or: as both part in both inequalities (\((r_1)^2>(r_2)^2\) and \(i_1*r_2>i_2*r_1\)) are positive then we can multiply them: \((r_1)^2*i_1*r_2>(r_2)^2*i_2*r_1\) > reduce by \(r_1r_2\) > \(i_1*r_1>i_2*r_2\). Sufficient. 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? Extrahard Quant Tests with Brilliant Analytics



Intern
Status: yet to apply
Joined: 05 Jun 2010
Posts: 15

Re: GMAT Club Test MGMAT Challenge Test 1 DS Question(#5)
[#permalink]
Show Tags
02 Oct 2010, 13:26
Well..No one till now commented on the possibility of negative interest rate??



CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2653
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35

Re: GMAT Club Test MGMAT Challenge Test 1 DS Question(#5)
[#permalink]
Show Tags
02 Oct 2010, 13:33
sibanmishra wrote: Well..No one till now commented on the possibility of negative interest rate?? ve interest rates are not possible for such investment. Do not over generalize the things on gmat.
_________________
Fight for your dreams :For all those who fear from Verbal lets give it a fight
Money Saved is the Money Earned
Jo Bole So Nihaal , Sat Shri Akaal
Support GMAT Club by putting a GMAT Club badge on your blog/Facebook
GMAT Club Premium Membership  big benefits and savings
Gmat test review : http://gmatclub.com/forum/670to710alongjourneywithoutdestinationstillhappy141642.html



Math Expert
Joined: 02 Sep 2009
Posts: 47977

Re: GMAT Club Test MGMAT Challenge Test 1 DS Question(#5)
[#permalink]
Show Tags
02 Oct 2010, 13:33



Intern
Joined: 08 Nov 2009
Posts: 15

Re: GMAT Club Test MGMAT Challenge Test 1 DS Question(#5)
[#permalink]
Show Tags
02 Oct 2010, 13:52
Hello Bunuel , Shrouded1 , What abt the following consideration . from (1) we know r1 > r2 so irrespective of i1 being greater or less than i2 , we would know that i1*r1 yields high value . Example Consider i1 > i2 (and we know r1 >r2 and i1 and i2 have to be positive values ). say i1 : 150 , i2 : 100 Value of Inv on X : i1*r1 : 150*5% : 7.5 Value of Inv on Y : i2*r2 : 100*3% : 3 Therefore X > Y Take the other case of i1< i2 ( and still r1 >r2 and i1 and i2 have to be positive values ). Say i1 : 100 , i2 : 150 Value of Inv on X : i1*r1 : 100*5% : 5 Value of Inv on Y : i2*r2 : 150*3% : 4.5 So it does not matter what is the principle amount hence (A) or stmnt 1 is sufficient . Where am I going wrong ?
PS : Gurpreet I have corrected the OA .Sorry abt that .



Math Expert
Joined: 02 Sep 2009
Posts: 47977

Re: GMAT Club Test MGMAT Challenge Test 1 DS Question(#5)
[#permalink]
Show Tags
02 Oct 2010, 14:05
nandini11 wrote: Hello Bunuel , Shrouded1 , What abt the following consideration . from (1) we know r1 > r2 so irrespective of i1 being greater or less than i2 , we would know that i1*r1 yields high value . Example Consider i1 > i2 (and we know r1 >r2 and i1 and i2 have to be positive values ). say i1 : 150 , i2 : 100 Value of Inv on X : i1*r1 : 150*5% : 7.5 Value of Inv on Y : i2*r2 : 100*3% : 3 Therefore X > Y Take the other case of i1< i2 ( and still r1 >r2 and i1 and i2 have to be positive values ). Say i1 : 100 , i2 : 150 Value of Inv on X : i1*r1 : 100*5% : 5 Value of Inv on Y : i2*r2 : 150*3% : 4.5 So it does not matter what is the principle amount hence (A) or stmnt 1 is sufficient . Where am I going wrong ?
PS : Gurpreet I have corrected the OA .Sorry abt that . That's not correct. Are you saying that interest earned depends only on interest rate? So if I ask you what would you prefer 1% annual interest from $1,000,000,000 or 100% annual interest from $1?
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 06 Jun 2009
Posts: 313
Location: USA
WE 1: Engineering

Re: GMAT Club Test MGMAT Challenge Test 1 DS Question(#5)
[#permalink]
Show Tags
02 Oct 2010, 14:31
Quote: That's not correct. Are you saying that interest earned depends only on interest rate?
So if I ask you what would you prefer 1% annual interest from $1,000,000,000 or 100% annual interest from $1? Bunuel, I will be more than happy to accept the former with only 0.25%
_________________
All things are possible to those who believe.



Intern
Joined: 08 Nov 2009
Posts: 15

Re: GMAT Club Test MGMAT Challenge Test 1 DS Question(#5)
[#permalink]
Show Tags
02 Oct 2010, 14:32
I get it now .My choice of plugin numbers was not comprehensive enuf . Thanks a lot Bunuel .



Senior Manager
Joined: 06 Jun 2009
Posts: 313
Location: USA
WE 1: Engineering

Re: GMAT Club Test MGMAT Challenge Test 1 DS Question(#5)
[#permalink]
Show Tags
02 Oct 2010, 14:38
nandini11 wrote: Hello Bunuel , Shrouded1 , What abt the following consideration . from (1) we know r1 > r2 so irrespective of i1 being greater or less than i2 , we would know that i1*r1 yields high value . Example Consider i1 > i2 (and we know r1 >r2 and i1 and i2 have to be positive values ). say i1 : 150 , i2 : 100 Value of Inv on X : i1*r1 : 150*5% : 7.5 Value of Inv on Y : i2*r2 : 100*3% : 3 Therefore X > Y Take the other case of i1< i2 ( and still r1 >r2 and i1 and i2 have to be positive values ). Say i1 : 100 , i2 : 150 Value of Inv on X : i1*r1 : 100*5% : 5 Value of Inv on Y : i2*r2 : 150*3% : 4.5 So it does not matter what is the principle amount hence (A) or stmnt 1 is sufficient . Where am I going wrong ?
PS : Gurpreet I have corrected the OA .Sorry abt that . Nandini, the numbers you have taken in this particular case are playing the trick. In your example, the ratio of the R's and I's are peculiar. Take extreme example. If you think i1 & i2 do not matter. Do this: Case 1 i1=$10000 and i2=$100 r1=5% and r2=4.99% .. as a result r1>r2 Value of return ......... X = 10000*5% = $500 Y = 100*4.99% = $4.99 X >> Y Case 2 i1=$100 and i2=$10000 r1=5% and r2=4.99% .. as a result r1>r2 Value of return ......... X = 100*5% = $5 Y = 10000*4.99% = $499 X << Y
_________________
All things are possible to those who believe.



Intern
Joined: 10 Dec 2013
Posts: 20
Location: India
Concentration: Technology, Strategy
GPA: 3.9
WE: Consulting (Consulting)

Re: Samantha invests i1 dollars in bond X, which pays r1
[#permalink]
Show Tags
01 Mar 2014, 14:03
Can the rates R1 and R2 be fractions? In that case R1^2 > R2^2 would not necessarily mean R1>R2.



Math Expert
Joined: 02 Sep 2009
Posts: 47977

Re: Samantha invests i1 dollars in bond X, which pays r1
[#permalink]
Show Tags
02 Mar 2014, 04:26



SVP
Joined: 06 Sep 2013
Posts: 1851
Concentration: Finance

Re: Samantha invests i1 dollars in bond X, which pays r1
[#permalink]
Show Tags
29 Mar 2014, 09:06
Is i1r1>i2r2?
Statement 1
ri>r2
This is clearly insufficient
Statement 2
i1/i2>r1/r2
i1r2>r1i2.
Insufficient on its own
Now both together
i1r2>r1i2 r1>r2
Multiplying inequalities since we know both sides are positive then simplifying we get
i2>i2
Since we know that r1>r2 as well then
i1r1>i2r2
Sufficient
C
Hope this helps Cheers J



Director
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 871
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)

Re: Samantha invests i1 dollars in bond X, which pays r1
[#permalink]
Show Tags
14 Apr 2014, 09:48
Read to eat stuff: it will refresh your concept and keep you away from any confusion during exam. Kudos me if it is helpful. Attachment:
Ratio properties.jpg [ 81.01 KiB  Viewed 2342 times ]
_________________
Piyush K
 Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison Don't forget to press> Kudos My Articles: 1. WOULD: when to use?  2. All GMATPrep RCs (New) Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6028
GPA: 3.82

Re: Samantha invests i1 dollars in bond X, which pays r1
[#permalink]
Show Tags
02 Apr 2018, 23:08
nandini11 wrote: Samantha invests i1 dollars in bond X, which pays r1 percent simple interest annually, and she invests i2 dollars in bond Y, which pays r2 percent simple interest annually. After one year, will she have earned more interest, in dollars, from bond X than from bond Y ? (1) \((r1)^2 > (r2)^2\) (2) The ratio of i1 to i2 is larger than the ratio of r1 to r2 . Why cant 1 be sufficient . We know that interest cannot be negative , therefore (1) eventually leads to r1> r2 . The values of i1 and I2 don’t matter , because even when i2 is greater than i1 , the interest would be less .Eg. i1 : 100 r1: 5% , i2: 150 , r2: 3% , i1r1 > i2r2 giving the required result . Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Since we have 4 variables (i1, i2, r1 and r2) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) and 2): Since r1 and r2 are positive, (r1)^2 > (r2)^2 implies r1 > r2 or r1/r2 > 1. Since i1/i2 > r1/r2 from the condition 2), i1/i2 > r1/r2 > 1 implies i1/i2 > 1 or i1 > i2. i1 * r1 > i2 * r2. Thus the interest from the bond X is more than the interest from the bond Y. Both conditions together are sufficient. Therefore, C is the answer. In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"




Re: Samantha invests i1 dollars in bond X, which pays r1 &nbs
[#permalink]
02 Apr 2018, 23:08






