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Is x less than 20?

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Is x less than 20? [#permalink] New post 20 Mar 2012, 08:07
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Question Stats:

77% (01:27) correct 23% (24:59) wrong based on 159 sessions
Is x less than 20?

(1) The sum of x and y is less than 20.
(2) y is less than 20.
[Reveal] Spoiler: OA

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Re: Is x less than 20? [#permalink] New post 20 Mar 2012, 08:17
Expert's post
enigma123 wrote:
Is x < 20?

1. Sum of x and y is less than 20

2. y is less than 20

How come the answer is E and not A?


Consider two cases:
x=30 and y=-15;
x=15 and y=-15;

Both examples satisfy the statements and give different answers to the question whether x<20. Not sufficient.

Answer: E.
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Is x less than 20? [#permalink] New post 04 Feb 2014, 20:56
nfa1rhp wrote:
Is x less than 20?

1) The sum of x and y is less than 20

2) y is less than 20

I thought working together they would be sufficient but they are not.
[/quote]

Ans E

1 & 2 not sufficient : as difference of two numbers does not implicate their magnitude in any way
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Re: Is x less than 20? [#permalink] New post 01 Mar 2014, 13:16
but if we solve it like this:
subtract
x+y < 20
y < 20

x+y-y<0
x<0

then x will be certainly less than 20...

Why is this approach flawed ?

Bunuel wrote:
enigma123 wrote:
Is x < 20?

1. Sum of x and y is less than 20

2. y is less than 20

How come the answer is E and not A?


Consider two cases:
x=30 and y=-15;
x=15 and y=-15;

Both examples satisfy the statements and give different answers to the question whether x<20. Not sufficient.

Answer: E.
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Re: Is x less than 20? [#permalink] New post 02 Mar 2014, 03:20
Expert's post
mariofelix wrote:
but if we solve it like this:
subtract
x+y < 20
y < 20

x+y-y<0
x<0

then x will be certainly less than 20...

Why is this approach flawed ?

Bunuel wrote:
enigma123 wrote:
Is x < 20?

1. Sum of x and y is less than 20

2. y is less than 20

How come the answer is E and not A?


Consider two cases:
x=30 and y=-15;
x=15 and y=-15;

Both examples satisfy the statements and give different answers to the question whether x<20. Not sufficient.

Answer: E.


That's wrong because you cannot subtract inequalities with signs in the same direction.

ADDING/SUBTRACTING INEQUALITIES:


You can only add inequalities when their signs are in the same direction:

If a>b and c>d (signs in same direction: > and >) --> a+c>b+d.
Example: 3<4 and 2<5 --> 3+2<4+5.

You can only apply subtraction when their signs are in the opposite directions:

If a>b and c<d (signs in opposite direction: > and <) --> a-c>b-d (take the sign of the inequality you subtract from).
Example: 3<4 and 5>1 --> 3-5<4-1.

Adding/subtracting/multiplying/dividing inequalities: help-with-add-subtract-mult-divid-multiple-inequalities-155290.html


Hope it helps.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Question about DS - Is x less than 20? [#permalink] New post 21 Jul 2014, 15:55
Hi All,

I have a question regarding a data sufficiency problem.

Is x less than 20?

1) x + y < 20
2) y is less than 20


My question refers to 1.). In this case, since it says x + y, can we plug in a negative number in for y even with a + sign in front of it?

ex. if x=25, y=-8,
25 + (-8) = 17
we do not know if x<20, therefore INSUFFICIENT

I am sure this question is pretty basic to most, but it is these small details that seem to throw me off while solving DS problems. Any advice would be very helpful.

BTW - This question is from the CAT on GMATPrep software.

Thanks,
Mike
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Re: Is x less than 20? [#permalink] New post 22 Jul 2014, 02:24
Expert's post
MikeA2606 wrote:
Hi All,

I have a question regarding a data sufficiency problem.

Is x less than 20?

1) x + y < 20
2) y is less than 20


My question refers to 1.). In this case, since it says x + y, can we plug in a negative number in for y even with a + sign in front of it?

ex. if x=25, y=-8,
25 + (-8) = 17
we do not know if x<20, therefore INSUFFICIENT

I am sure this question is pretty basic to most, but it is these small details that seem to throw me off while solving DS problems. Any advice would be very helpful.

BTW - This question is from the CAT on GMATPrep software.

Thanks,
Mike


Merging similar topics. Please refer to the discussion above.

As for your question: y is some number, it could be negative, positive or 0. So, you can plug any number you want there.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 3, and 7. Thank you.


_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: Is x less than 20?   [#permalink] 22 Jul 2014, 02:24
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