GMAT Changed on April 16th - Read about the latest changes here

 It is currently 24 Apr 2018, 00:01

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# M18-19

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44652

### Show Tags

16 Sep 2014, 01:03
Expert's post
14
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

34% (01:17) correct 66% (00:57) wrong based on 231 sessions

### HideShow timer Statistics

If $$S$$ and $$T$$ are non-zero numbers and $$\frac{1}{S} + \frac{1}{T} = S + T$$, which of the following must be true?

A. $$ST = 1$$
B. $$S + T = 1$$
C. $$\frac{1}{S} = T$$
D. $$\frac{S}{T} = 1$$
E. none of the above
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 44652

### Show Tags

16 Sep 2014, 01:03
Expert's post
1
This post was
BOOKMARKED
Official Solution:

If $$S$$ and $$T$$ are non-zero numbers and $$\frac{1}{S} + \frac{1}{T} = S + T$$, which of the following must be true?

A. $$ST = 1$$
B. $$S + T = 1$$
C. $$\frac{1}{S} = T$$
D. $$\frac{S}{T} = 1$$
E. none of the above

$$\frac{1}{S} + \frac{1}{T} = S + T$$;

$$\frac{T+S}{ST}=S+T$$$$\rightarrow$$;

Cross-multiply: $$S+T=(S+T)*ST$$;

$$(S+T)(ST-1)=0$$. Either $$S+T=0$$ or $$ST=1$$. Now, notice that if $$S+T=0$$ is true then none of the options must be true.

_________________
Current Student
Joined: 01 Aug 2014
Posts: 41
Location: India
GPA: 3.65

### Show Tags

13 Nov 2014, 21:16
Hello Bunuel,

I have one doubt in this question. when we say "non zero numbers", does it always mean non zero counting numbers (i.e > 0) or non zero real numbers (+ve and -ve)?
as in later scenatio ST can be 1, S = +/-1 and T =+/-1 and statement holds true. and if its former scenario then "none" remains the only choice when S != T.

Can you help me make sense of inferences, as I think I am over thinking and confused with many inferences.

rgds,
Math Expert
Joined: 02 Sep 2009
Posts: 44652

### Show Tags

14 Nov 2014, 02:34
Alaukik wrote:
Hello Bunuel,

I have one doubt in this question. when we say "non zero numbers", does it always mean non zero counting numbers (i.e > 0) or non zero real numbers (+ve and -ve)?
as in later scenatio ST can be 1, S = +/-1 and T =+/-1 and statement holds true. and if its former scenario then "none" remains the only choice when S != T.

Can you help me make sense of inferences, as I think I am over thinking and confused with many inferences.

rgds,

A nonzero number is a number which is NOT 0, so it can be any real number except 0, positive or negative.
_________________
Current Student
Joined: 01 Aug 2014
Posts: 41
Location: India
GPA: 3.65

### Show Tags

14 Nov 2014, 03:31
Bunuel wrote:
Alaukik wrote:
Hello Bunuel,

I have one doubt in this question. when we say "non zero numbers", does it always mean non zero counting numbers (i.e > 0) or non zero real numbers (+ve and -ve)?
as in later scenatio ST can be 1, S = +/-1 and T =+/-1 and statement holds true. and if its former scenario then "none" remains the only choice when S != T.

Can you help me make sense of inferences, as I think I am over thinking and confused with many inferences.

rgds,

A nonzero number is a number which is NOT 0, so it can be any real number except 0, positive or negative.

so the answer has to be ST = 1? right?
Math Expert
Joined: 02 Sep 2009
Posts: 44652

### Show Tags

14 Nov 2014, 05:36
Alaukik wrote:
Bunuel wrote:
Alaukik wrote:
Hello Bunuel,

I have one doubt in this question. when we say "non zero numbers", does it always mean non zero counting numbers (i.e > 0) or non zero real numbers (+ve and -ve)?
as in later scenatio ST can be 1, S = +/-1 and T =+/-1 and statement holds true. and if its former scenario then "none" remains the only choice when S != T.

Can you help me make sense of inferences, as I think I am over thinking and confused with many inferences.

rgds,

A nonzero number is a number which is NOT 0, so it can be any real number except 0, positive or negative.

so the answer has to be ST = 1? right?

No. Consider S = 2 and T = -2. In this case none of the options are true. The correct answer is E.
_________________
Current Student
Joined: 01 Aug 2014
Posts: 41
Location: India
GPA: 3.65

### Show Tags

14 Nov 2014, 06:36
aah ok. got it thanks.
Manager
Joined: 20 Jan 2014
Posts: 164
Location: India
Concentration: Technology, Marketing

### Show Tags

02 Jan 2015, 10:04
Bunuel wrote:
Official Solution:

If $$S$$ and $$T$$ are non-zero numbers and $$\frac{1}{S} + \frac{1}{T} = S + T$$, which of the following must be true?

A. $$ST = 1$$
B. $$S + T = 1$$
C. $$\frac{1}{S} = T$$
D. $$\frac{S}{T} = 1$$
E. none of the above

$$\frac{1}{S} + \frac{1}{T} = S + T$$;

$$\frac{T+S}{ST}=S+T$$$$\rightarrow$$;

Cross-multiply: $$S+T=(S+T)*ST$$;

$$(S+T)(ST-1)=0$$. Either $$S+T=0$$ or $$ST=1$$. Now, notice that if $$S+T=0$$ is true then none of the options must be true.

How can we cross multiply ST, ST can be negative as well
_________________

Consider +1 Kudos Please

Math Expert
Joined: 02 Sep 2009
Posts: 44652

### Show Tags

05 Jan 2015, 05:43
him1985 wrote:
Bunuel wrote:
Official Solution:

If $$S$$ and $$T$$ are non-zero numbers and $$\frac{1}{S} + \frac{1}{T} = S + T$$, which of the following must be true?

A. $$ST = 1$$
B. $$S + T = 1$$
C. $$\frac{1}{S} = T$$
D. $$\frac{S}{T} = 1$$
E. none of the above

$$\frac{1}{S} + \frac{1}{T} = S + T$$;

$$\frac{T+S}{ST}=S+T$$$$\rightarrow$$;

Cross-multiply: $$S+T=(S+T)*ST$$;

$$(S+T)(ST-1)=0$$. Either $$S+T=0$$ or $$ST=1$$. Now, notice that if $$S+T=0$$ is true then none of the options must be true.

How can we cross multiply ST, ST can be negative as well

Notice that we have an equation, not an inequality. So, it does not matter whether ST is negative. Only for inequalities we should flip the sign when multiplying by negative value.
_________________
Intern
Joined: 04 Mar 2010
Posts: 9

### Show Tags

18 Apr 2015, 17:31
1
This post was
BOOKMARKED
When we solve we get 'Either S+T=0 or ST=1'. So, any of these is correct. We have 'ST=1' as option (A), why it is not correct? Please let me know!
Math Expert
Joined: 02 Sep 2009
Posts: 44652

### Show Tags

19 Apr 2015, 03:45
reddyMBA wrote:
When we solve we get 'Either S+T=0 or ST=1'. So, any of these is correct. We have 'ST=1' as option (A), why it is not correct? Please let me know!

Because it's not necessary that st=1. If s+t=0, then st could be some other number but 1.
_________________
Director
Joined: 10 Mar 2013
Posts: 563
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)

### Show Tags

14 Oct 2015, 14:19
I have doubts with this question.. have same problem as others here: after manipulations we get the same expression st=1 like in the answer choice, and we see such questions very often by GMAT, and the right answer is just a manipulated version of the question.
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Manager
Joined: 05 Jul 2015
Posts: 105
Concentration: Real Estate, International Business
GMAT 1: 600 Q33 V40
GPA: 3.3

### Show Tags

20 Feb 2016, 21:03
1
KUDOS
I found the plug-in numbers method to be more effective for this problem.

If you plug in -1 for S and 1 for T you'll see that none of the options work.
Current Student
Joined: 12 May 2016
Posts: 2
Schools: HBS '18 (A)

### Show Tags

26 May 2016, 19:29
When I did this question I noticed that if you reduce by S+T and ended up with ST = 1, you'll see that 1/S = T is the same solution. That tipped me off.
Senior Manager
Joined: 31 Mar 2016
Posts: 404
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

### Show Tags

27 Aug 2016, 06:12
I think this is a high-quality question and I agree with explanation.
Manager
Joined: 21 Apr 2016
Posts: 187

### Show Tags

05 Sep 2016, 11:57
when you have an equation (x-3)(x-2) = 0; x is either 3 or 2.

(S+T)(ST-1) = 0; => S+T = 0; or ST = 1;

ST = 1 should be the answer. However, S = 1/T is the same. So looks like there is more than one correct answer to this question!!
Intern
Joined: 04 Dec 2015
Posts: 7

### Show Tags

02 Mar 2017, 04:48
Hi Bunuel ,
I fell in the same pitfall as many other users did.

Simplifying S+T is basically letting us get rid of a possible solution, which is exactly what the question wants us to do to take the wrong path.
My question is: how do we notice that a certain algebraic operation is going to neglect a potential solution? Can we assume as a rule-of-thumb that multiplying is always more reliable than dividing unknown values?

Many thanks, great question by the way.
Manager
Joined: 26 Nov 2016
Posts: 52

### Show Tags

27 Jun 2017, 10:05
Great question! I'm not happy to get it wrong, but I'm happy to have learned the proper way to do it correctly in the future.

I got as far as trying to rationalize the denominator of the 1/S + 1/T. But then after that, I had no idea what to do. I didn't think that bringing them both to one side and setting the other equal to zero was the way to solve it.

Nice~
SVP
Joined: 26 Mar 2013
Posts: 1613

### Show Tags

27 Jun 2017, 15:19
Bunuel wrote:
If $$S$$ and $$T$$ are non-zero numbers and $$\frac{1}{S} + \frac{1}{T} = S + T$$, which of the following must be true?

A. $$ST = 1$$
B. $$S + T = 1$$
C. $$\frac{1}{S} = T$$
D. $$\frac{S}{T} = 1$$
E. none of the above

Another approach for this great problem

Non-zero integers means negative or positive integers

Let see apply some cases with numbers to DISAPPROVE answer choices

S = T = 1............Equation is 2 = 2

S = T =-1............Equation is -2 = -2

S = 1 & T =-1....Equation is 0 = 0 or S = -1 & T =1....Equation is 0 = 0

A. $$ST = 1$$ ............Case 3 does not apply....................Eliminate A

B. $$S + T = 1$$........No cases applies.............................Eliminate B

C. $$\frac{1}{S} = T$$ .......Case 3 does not apply...........Eliminate C

D. $$\frac{S}{T} = 1$$ .......Case 3 does not apply.....Eliminate D

E. none of the above...........Correct

Intern
Joined: 20 Aug 2017
Posts: 15

### Show Tags

12 Dec 2017, 07:46
Hey,

Can someone please clarify how did we get (S+T)(ST−1)=0?

here is the explanation again:

Cross-multiply: S+T=(S+T)∗ST

(S+T)(ST−1)=0

Thank you!
Re: M18-19   [#permalink] 12 Dec 2017, 07:46

Go to page    1   2    Next  [ 21 posts ]

Display posts from previous: Sort by

# M18-19

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

Moderators: chetan2u, Bunuel

 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®.