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If a > b and c < d , which of the following MUST be true?
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10 Sep 2019, 21:38
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Competition Mode Question 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. \(a^2+d^2>b^2+c^2\)
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Re: If a > b and c < d , which of the following MUST be true?
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10 Sep 2019, 22:35
given a > b and c < d
ab > 0 and cd < 0 from here we know that ab > cd
ac > bd
bd < ac
D is the correct answer



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Re: If a > b and c < d , which of the following MUST be true?
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10 Sep 2019, 22:41
Ans: D Because, a>b , c<d. In inequalities, opposite signs can be subtracted. Or, c<d > c>d . On adding a>b + (c>d) = ac>bd only d gives this answer choice



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Re: If a > b and c < d , which of the following MUST be true?
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10 Sep 2019, 22:49
We are given a>b and c<d, we are to determine which of the answer choices must be true. D is the answer. This is because a>b and c<d, hence bd will always be less than ac. We are subtracting a smaller number, c, from a, where a>b and subtracting a bigger number, d, where d>c from b. Definitely, ac will always be greater than bd.
In A, ad>cb, is not always true. when a=5, b=4, c=1, d=7, ad(2)>cb(3) however if a=5, b=4, c=6, and d=7; ad(2)<cb(3).
Similarly, in B, a+d>b is not always true. This is because, we don't know whether a,b, and d are greater than zero or otherwise. when a,b, and d are all greater than 0, then a+d>b. However, if a and b are positive and d is negative, it is possible than a+d<b. Hence B is not always true.
C b+c>ad. This is also not always true. Depending on the magnitudes of a,b,c, and d, b+c>ad. in other instances, b+c<ad. To illustrate, let a=5, b=4, c=6 and d=7 then b+c(10)>ad(2). However, if a=5, b=4, c=6 and d=1, then b+c(2)<ad(6)
E a^2 + d^2 > b^2 + c^2. This is not always true. It is true for a,b,c, and d greater than zero. However, if a,b,c, and d are all negative, then it is not true.



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Re: If a > b and c < d , which of the following MUST be true?
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10 Sep 2019, 23:48
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. \(a^2+d^2>b^2+c^2\) a>b d>c a+d>b+c bd<ac IMO D
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Re: If a > b and c < d , which of the following MUST be true?
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11 Sep 2019, 03:31
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. \(a^2 + d^2 > b^2 + c^2\) Following cases are possible: 1. b < a < c < d 2. c < d < b < a 3. b < a = c < d 4. c < d = b < a 5. b < c < a = d 6. c < b < a = d 7. b = c < a < d 8. b = c < d < a Attachment: File comment: abcd
abcd.JPG [ 30.76 KiB  Viewed 820 times ]
Only case 1 and 2 are sufficient. Answer (D).
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Re: If a > b and c < d , which of the following MUST be true?
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11 Sep 2019, 05:45
Quote: 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. \(a^2+d^2>b^2+c^2\) given: a>b and c<d have different signs, we can subtract them, maintaining the former sign. a>b(c<d)=ac>bd…bd<ac Answer (D)



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Re: If a > b and c < d , which of the following MUST be true?
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11 Sep 2019, 07:17
If a>b and c<d, which of the following MUST be true? a>b > ab>0  (1) c<d > d>c > dc>0 (2) add (1) + (2) (now, we can add because both (1) & (2) have > 0 on rhs) (ab)+(dc)>0 (a+d)(b+c)>0 (a+d)>(b+c) (3)
A. a−d>c−b Incorrect, after rearranging, we can't get (3) B. a+d>b Incorrect, we can't get (3) C. b+c>a−d Incorrect, we can't get (3) after rearranging D. b−d<a−c Correct, after rearranging, (b+c)<(a+d) > (a+d)>(b+c) which is (3) E. (a^2 +d^2) >(b^2 +c^2) Incorrect, we can't get (3) after rearranging



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Re: If a > b and c < d , which of the following MUST be true?
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11 Sep 2019, 08:22
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. \(a^2\)+\(d^2\)>\(b^2\)+\(c^2\)
Eq1 : a > b Eq2 : c<d ...Multiply both sides by 1, c > d Add 1 & 2  ac > bd
Scan the answer choices that match above expression
D it is.



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If a > b and c < d , which of the following MUST be true?
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02 Nov 2019, 14:17
Bunuel wrote: Competition Mode Question 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. \(a^2+d^2>b^2+c^2\) Nice question. Manipulate the answer choices to just be addition on both sides.A) \(a−d>c−b\) > a+b>c+d Clearly not necessarily true.B) \(a+d>b\) What if d is a high magnitude negative number? Example: a=1 b=0 d=100 c=101
1100>0.... Not trueC) \(b+c>a−d\) > b+c+d>a Clearly not necessarily true. Make a = a huge numberD) \(b−d<a−c\) > b+c<a+d True. Both sides are pure addition and the larger numbers are on the same side.E) \(a^2+d^2>b^2+c^2\) Trap Answer. What if our small numbers are high magnitude negative numbers? Example: a=0 b=10 d=0 c=10
0+0>100+100
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If a > b and c < d , which of the following MUST be true?
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02 Nov 2019, 14:17






