It is currently 21 Jan 2018, 22:41

### 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

# Is |s+t| < |s|+|t|?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4705
GPA: 3.82

### Show Tags

12 Dec 2017, 23:39
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

76% (00:33) correct 24% (01:10) wrong based on 68 sessions

### HideShow timer Statistics

[GMAT math practice question]

Is $$|s+t| < |s|+|t|$$?

1) $$s>t$$
2) $$st<0$$
[Reveal] Spoiler: OA

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Senior Manager
Joined: 15 Jan 2017
Posts: 360
Re: Is |s+t| < |s|+|t|? [#permalink]

### Show Tags

13 Dec 2017, 00:43
Im not sure how B is suff.

|-1 + 3| < |-1| + |3| --> 2 < 4 suff

|-1 + 3| < 1 - 3 (opening 3 as negative, -1 remains one) --> 2 not less than -2

We get two cases.

Senior Manager
Joined: 05 Dec 2016
Posts: 260
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: Is |s+t| < |s|+|t|? [#permalink]

### Show Tags

13 Dec 2017, 00:49
This inequality holds true if signs are different and none of the variables is Zero

(1) no information about the signs and actual values, so multiples outcomes are possible:
s=5 t=1
|5+1|=|5|+|1| answer is NO because we have an equality

s=5 t=-1
|5-1|<|5|+|1| answer is YES, signs are different

s=-5 t=0
again we have an equality so again the answer is NO

(2) now we get information that the signs of t & s, and that none if the variables is equal to Zero hence YES sufficicent

DS Forum Moderator
Joined: 21 Aug 2013
Posts: 675
Location: India

### Show Tags

13 Dec 2017, 10:07
Im not sure how B is suff.

|-1 + 3| < |-1| + |3| --> 2 < 4 suff

|-1 + 3| < 1 - 3 (opening 3 as negative, -1 remains one) --> 2 not less than -2

We get two cases.

Hi

I understand that you have plugged in certain values of s and t as -1 and 3 respectively. Your first case is correct, and that is how we will solve this. I did not understand 'opening 3 as negative', absolute value of 3 or |3| will be 3 only, not -3. And absolute value of |-1| will be 1, so RHS is 1+3 = 4.
Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 458
GMAT 1: 790 Q51 V49
GRE 1: 340 Q170 V170
Re: Is |s+t| < |s|+|t|? [#permalink]

### Show Tags

13 Dec 2017, 13:28
Im not sure how B is suff.

|-1 + 3| < |-1| + |3| --> 2 < 4 suff

|-1 + 3| < 1 - 3 (opening 3 as negative, -1 remains one) --> 2 not less than -2

We get two cases.

I think you've gotten turned around a little in how you're looking at absolute values.

If a problem says something like |x| = 3, then x can equal 3 or -3. So, if a problem tells you what |x| is, and asks you about the value of x, you do what you described here.

However, if you're putting a number (or any known value) inside of absolute value signs, then it will always become positive, no matter what. Since the problem talks about the value of |s| and the value of |t|, those two values, |s| and |t|, will always be positive numbers. Interpreting it as '1-3' is incorrect - it has to be 1 + 3 no matter what.
_________________

Chelsey Cooley | Manhattan Prep Instructor | Seattle and Online

My upcoming GMAT trial classes | GMAT blog archive

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4705
GPA: 3.82
Re: Is |s+t| < |s|+|t|? [#permalink]

### Show Tags

15 Dec 2017, 07:21
1
KUDOS
Expert's post
=>

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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Modifying the question:
$$|s+t| < |s|+|t|$$
$$⇔ |s+t|^2 < (|s|+|t|)^2$$
$$⇔ (s+t)^2 < (|s|+|t|)^2$$
$$⇔ s^2 + 2st + t^2 < |s|^2 + 2|s||t|+ |t|^2$$
$$⇔ s^2 + 2st + t^2 < s^2 + 2|s||t|+ t^2$$
$$⇔ 2st < 2|s||t|$$
$$⇔ st < |st|$$
$$⇔ st < 0$$

This is exactly condition 2).

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Re: Is |s+t| < |s|+|t|?   [#permalink] 15 Dec 2017, 07:21
Display posts from previous: Sort by