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If a > b and if c > d, then which of the following must be true?
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Updated on: 20 Jan 2019, 20:24
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68% (00:46) correct 32% (00:44) wrong based on 388 sessions
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Originally posted by carcass on 19 Mar 2012, 04:39.
Last edited by Bunuel on 20 Jan 2019, 20:24, edited 2 times in total.
Edited the question and the OA




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Re: If a > b and if c > d, then which of the following must be true?
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19 Mar 2012, 04:49
carcass wrote: If a > b and if c > d , then wich of the following must be true ??
1) ab > c+d 2) ac > bd 3) c+d < ab 4) b+d < a+c 5) ac < b+d
here the answer is E but i wonder if is incorrect because we add unequal quantities but should not be a + c > b+d ??? 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 \(<\)) > \(ac>bd\) (take the sign of the inequality you subtract from). Example: \(3<4\) and \(5>1\) > \(35<41\). BACK TO THE ORIGINAL QUESTION: If a > b and if c > d , then which of the following must be true? A. ab > c+d B. ac > bd C. c+d < ab D. b+d < a+c E. ac < b+d Since the signs of the inequalities are in the same direction we can add them: \(a+c>b+d\), which is the same as the option D: \(b+d < a+c\). So, the correct answer is D, not E. Answer: D. Hope its' clear.
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Re: If a > b and if c > d, then which of the following must be true?
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19 Mar 2012, 04:58
I think answer E is wrong here.
Is a > b and if c > d , then wich of the following must be true ??
1) ab > c+d 2) ac > bd 3) c+d < ab 4) b+d < a+c 5) ac < b+d
so i picked 100 > 1 and 3 > 2 to test E
1003<1+2 (FALSE)
I think D is answer



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Re: If a > b and if c > d, then which of the following must be true?
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19 Mar 2012, 06:02
Bunuel wrote: carcass wrote: If a > b and if c > d , then wich of the following must be true ??
1) ab > c+d 2) ac > bd 3) c+d < ab 4) b+d < a+c 5) ac < b+d
here the answer is E but i wonder if is incorrect because we add unequal quantities but should not be a + c > b+d ??? 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 \(<\)) > \(ac>bd\) (take the sign of the inequality you subtract from). Example: \(3<4\) and \(5>1\) > \(35<41\). BACK TO THE ORIGINAL QUESTION: If a > b and if c > d , then which of the following must be true? A. ab > c+d B. ac > bd C. c+d < ab D. b+d < a+c E. ac < b+d Since the signs of the inequalities are in the same direction we can add them: \(a+c>b+d\), which is the same as the option D: \(b+d < a+c\). So, the correct answer is D, not E. Answer: D. Hope its' clear. Infact Bunuel as you can see from my question above I pick the right answer D but something make me suspicious and I thought to ask here to you. This shows how is important to rely solely and exclusively on good gmat material. Thanks Mod.
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Re: If a > b and if c > d, then which of the following must be true?
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31 Oct 2012, 10:47
Algebraic Approach a>b ==> ab>0 (1) c>d ==> cd>0 (2) (1) + (2) ==> ab + cd > 0 (a+c) (b+d)>0 ==> (b+d) < (a+c)



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Re: If a > b and if c > d, then which of the following must be true?
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31 Jul 2015, 09:54
If a>b and c<d, which of the following MUST be true? a)a−d>c−b b)a+d>b c)b+c>a−d d)b−d<a−c e)a2+d2>b2+c2



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Re: If a > b and if c > d, then which of the following must be true?
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31 Jul 2015, 15:01
Hi All, To address the original prompt....In questions that include inequalities in this fashion, it's important to note that we know NOTHING about how A and B relate to C and D. For example, it could be that A is the biggest number, but it might be second biggest (behind C) or third biggest (behind C and D). As such, what MUST be true will likely involve combining the bigger variables from each pair and the smaller variables in each pair. Since A > B and C > D, adding A and C will lead to a sum that MUST be greater than the sum of B and D. Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: If a > b and if c > d, then which of the following must be true?
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06 Jan 2019, 22:49
Bunuel wrote: carcass wrote: If a > b and if c > d , then wich of the following must be true ??
1) ab > c+d 2) ac > bd 3) c+d < ab 4) b+d < a+c 5) ac < b+d
here the answer is E but i wonder if is incorrect because we add unequal quantities but should not be a + c > b+d ??? 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 \(<\)) > \(ac>bd\) (take the sign of the inequality you subtract from). Example: \(3<4\) and \(5>1\) > \(35<41\). BACK TO THE ORIGINAL QUESTION: If a > b and if c > d , then which of the following must be true? A. ab > c+d B. ac > bd C. c+d < ab D. b+d < a+c E. ac < b+d Since the signs of the inequalities are in the same direction we can add them: \(a+c>b+d\), which is the same as the option D: \(b+d < a+c\). So, the correct answer is D, not E. Answer: D. Hope its' clear. I was solving this question by taking some values: a=2; b=1; c=1; d=100 Then b+d=101 & a+c=3 ; Clearly b+d < a+c doesn't hold in this case. Please share your thoughts.



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Re: If a > b and if c > d, then which of the following must be true?
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07 Jan 2019, 01:10
AVNISH2123 wrote: Bunuel wrote: carcass wrote: If a > b and if c > d , then wich of the following must be true ??
1) ab > c+d 2) ac > bd 3) c+d < ab 4) b+d < a+c 5) ac < b+d
here the answer is E but i wonder if is incorrect because we add unequal quantities but should not be a + c > b+d ??? 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 \(<\)) > \(ac>bd\) (take the sign of the inequality you subtract from). Example: \(3<4\) and \(5>1\) > \(35<41\). BACK TO THE ORIGINAL QUESTION: If a > b and if c > d , then which of the following must be true? A. ab > c+d B. ac > bd C. c+d < ab D. b+d < a+c E. ac < b+d Since the signs of the inequalities are in the same direction we can add them: \(a+c>b+d\), which is the same as the option D: \(b+d < a+c\). So, the correct answer is D, not E. Answer: D. Hope its' clear. I was solving this question by taking some values: a=2; b=1; c=1; d=100Then b+d=101 & a+c=3 ; Clearly b+d < a+c doesn't hold in this case. Please share your thoughts. The question says that: c > d.
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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: If a > b and if c > d, then which of the following must be true?
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07 Jan 2019, 01:24
I was solving this question by taking some values: a=2; b=1; c=1; d=100Then b+d=101 & a+c=3 ; Clearly b+d < a+c doesn't hold in this case. Please share your thoughts. [/quote] The question says that: c > d.[/quote] Apologies! While assigning the values, I was looking at the below question (from Veritas prep) which is very similar to the above stated one: If a>b and c<d, which of the following MUST be true? (A) ad>cb (B) a+d>b (C) b+c>ad (D) bd<ac (E) a^2 + d^2 > b^2 + c^2 Veritas Prep Ans D And the assigned values holds true for (D). Thanks Bunuel for your response!




Re: If a > b and if c > d, then which of the following must be true? &nbs
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