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Millis79
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Is A+2B < C + 2D? 12 Feb 2014, 18:12
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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5% (low)

Question Stats:

83% (00:54) correct 17% (01:00) wrong based on 228 sessions

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Is A+2B < C + 2D?

(1) A < C
(2) D > B
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C
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pradeepss
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Is A+2B < C + 2D? 12 Feb 2014, 19:35
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I will go with E

1&2 are clearly not sufficient. A=1 and c=100 and d=50 and b=0.5 then equality does not hold. Although a=1 and c=2 and d=100 and b=1 then equality holds. Clearly insufficient to answer the question without real values of abcd


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KarishmaB
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Is A+2B < C + 2D? 12 Feb 2014, 22:45
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Millis79
All,

I need some assistance on the below question:

Is A+2B < C + 2D?

(1) A < C
(2) D > B

Statement 1 alone doesn't tell you anything about B and D and statement 2 alone doesn't tell you anything about A and C so neither statement alone is sufficient.

Using both together,
A < C ....(I)
B < D (multiply this by 2. Note that we can multiply an inequality by a positive number. If we multiply by a negative number, the sign of the inequality flips)
2B < 2D ....(II)

Add (I) and (II) to get
A + 2B < C + 2D
We can answer the question with 'Yes' and hence both statement together are sufficient to answer.

Answer (C)
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Is A+2B < C + 2D? 12 Feb 2014, 23:24
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Millis79
All,

I need some assistance on the below question:

Is A+2B < C + 2D?

(1) A < C
(2) D > B


Statement I is insufficient as it does not say anything about B and D. Same goes for statement II.
Combining is sufficient:

Since C is greater than A and D is greater than B we can say that A + 2B < C + 2D
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Is A+2B < C + 2D? 13 Feb 2014, 01:14
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Is A+2B < C + 2D?

(1) A < C
(2) D > B

Clearly, the two statements individually are not sufficient. We just need to check if these together help us to answer the question or not.
Equation 1: A<C
Equation 2: B<D

Multiplying equation 2 by 2 and adding equation 1, we get:
A+2B < C + 2D

Hence, the two statements combined are sufficient to answer.
Option C

Thanks & Regards,
Sumiti Singh
Mnemonic Education Pvt Ltd
ssingh@mnemoniceducation.com
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Is A+2B < C + 2D? 14 Feb 2014, 05:17
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Tricky one, if you miss the GT or LT sign, you probably will be trapped, C is the right answer.
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Is A+2B < C + 2D? 28 Mar 2015, 08:23
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I ran into this problem while studying and I'm quite confused as to why you double the second statement once you combine the two. I understand how to get here a+b<c+d but do not understand why you double "b" and "d". This seems random to me and looks like it's only done to match the target question. Couldn't I double "a" and "c" also if I wanted to?

The explanation in the MGMAT book isn't helping me because it just tells you to double "b" and "d" or multiply them by 2 once you combine them but why??? Is there a rule or guideline to follow?
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Is A+2B < C + 2D? 30 Mar 2015, 02:35
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GmatFear
I ran into this problem while studying and I'm quite confused as to why you double the second statement once you combine the two. I understand how to get here a+b<c+d but do not understand why you double "b" and "d". This seems random to me and looks like it's only done to match the target question. Couldn't I double "a" and "c" also if I wanted to?

The explanation in the MGMAT book isn't helping me because it just tells you to double "b" and "d" or multiply them by 2 once you combine them but why??? Is there a rule or guideline to follow?

If you have an equation, can you multiply it by 2 on both sides without changing it? Sure.
x = 5
2x = 10

When you have an inequality, you can multiply it by a positive number on both sides without changing it.
x < 5
2x < 10
No matter what x is, if x is less than 5, 2x will be less than 10.

The question stem deals with 2B and 2D. So given that B < D, it implies that 2B must be less than 2D i.e. 2B < 2D. This helps us arrive at our answer. We can manipulate equations/inequalities to help us arrive at the answer.

You could double A and C too (2A < 2C) but that wouldn't help you get to the answer. You manipulate equations/inequalities (without changing them) to get what you want.
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Is A+2B < C + 2D? 30 Mar 2015, 16:16
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VeritasPrepKarishma
GmatFear
I ran into this problem while studying and I'm quite confused as to why you double the second statement once you combine the two. I understand how to get here a+b<c+d but do not understand why you double "b" and "d". This seems random to me and looks like it's only done to match the target question. Couldn't I double "a" and "c" also if I wanted to?

The explanation in the MGMAT book isn't helping me because it just tells you to double "b" and "d" or multiply them by 2 once you combine them but why??? Is there a rule or guideline to follow?

If you have an equation, can you multiply it by 2 on both sides without changing it? Sure.
x = 5
2x = 10

When you have an inequality, you can multiply it by a positive number on both sides without changing it.
x < 5
2x < 10
No matter what x is, if x is less than 5, 2x will be less than 10.

The question stem deals with 2B and 2D. So given that B < D, it implies that 2B must be less than 2D i.e. 2B < 2D. This helps us arrive at our answer. We can manipulate equations/inequalities to help us arrive at the answer.

You could double A and C too (2A < 2C) but that wouldn't help you get to the answer. You manipulate equations/inequalities (without changing them) to get what you want.

Your explanation makes perfect sense, thank you!
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Is A+2B < C + 2D? 02 Jul 2019, 01:01
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A+2B < C + 2D
--> A - C < 2D -2B
--> A - C < 2 (D - B)

(1) A < C
---> A - C < 0 ----> No info about D & B --->NS

(2) D > B
---> D - B > 0 ----->No info about A & C ----> NS

(1) + (2): A - C < D - B and it's obvious that A - C < 2 (D - B)
--->The answer is C
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Is A+2B < C + 2D? 20 Jun 2022, 11:23
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