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Re: If 4<(7-x)/3, which of the following must be true?
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 10 Mar 2016, 10:59
[quote="mn2010"]If 4<(7-x)/3, which of the following must be true? I. 5<x II. |x+3|>2 III. -(x+5) is positive A) II only B) III only C) I and II only D) II and III only E) I, II and III Hey Everyone I am facing majo issues with this one .. the second statement specifies X>1 or X<-5 now x can be 100 too hence it will make the inequality insufficient... I am rooting for B only Someone i the thread mentioned X<-5 is given right... but what if X is 100 .. i have every statement in this thread and still believe the answer is B .. Can anyone tell me where am i doing wrong P.S => DON'T tell me X<-5 IS GIVEN
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Re: If 4<(7-x)/3, which of the following must be true?
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20 Mar 2016, 14:54
try to plug in any number less than -5 and check because that's the condition given in question.
x < -5 means x can be -6,-7,-8 ....
|x+3|>2
when x= -6 => |-6+3|>2 true
when x=-100 => |-100+3|>2 true
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Re: If 4<(7-x)/3, which of the following must be true?
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01 Apr 2016, 02:17
Bunuel wrote: Bunuel wrote: mn2010 wrote: If 4<[(7-x)/3], which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive
A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III
I am not confused about statement II ???? Good question, +1. Note that we are asked to determine which MUST be true, not could be true. \(4<\frac{7-x}{3}\) --> \(12<7-x\) --> \(x<-5\). So we know that \(x<-5\), it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range \(x<-5\). Basically the question asks: if \(x<-5\) which of the following is true? I. \(5<x\) --> not true as \(x<-5\). II. \(|x+3|>2\), this inequality holds true for 2 cases, (for 2 ranges): 1. when \(x+3>2\), so when \(x>-1\) or 2. when \(-x-3>2\), so when \(x<-5\). We are given that second range is true (\(x<-5\)), so this inequality holds true. Or another way: ANY \(x\) from the range \(x<-5\) (-5.1, -6, -7, ...) will make \(|x+3|>2\) true, so as \(x<-5\), then \(|x+3|>2\) is always true. III. \(-(x+5)>0\) --> \(x<-5\) --> true. Answer: D. Hope it's clear. Yes. Basically we are given that x<-5 and then asked whether |x+3|>2 is true. We know that if x < -5, then |x+3|>2 must be true. Chiragjordan wrote: mn2010 wrote: If 4<(7-x)/3, which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive
A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III
Hey Everyone I am facing majo issues with this one ..
the second statement specifies X>1 or X<-5
now x can be 100 too hence it will make the inequality insufficient...
I am rooting for B only
Someone i the thread mentioned X<-5 is given right... but what if X is 100 ..
i have every statement in this thread and still believe the answer is B ..
Can anyone tell me where am i doing wrong
P.S => DON'T tell me X<-5 IS GIVEN Bunuel, Sorry that bother you but, in my humble opinion, it seems that Chiragjordan is correct. II is not true. A simple check can prove it : From II we have that Case A: x > -1 OR Case B: x < -5 From Case A let's take x = 0 4<[(7-x)/3] => 4<[(7-0)/3] - is not true => Case A => is not working Because problem's type is MUST BE not COULD BE => the answer is B ( only III MUST BE true ) . Bunuel, please, could you confirm ?
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Re: If 4<(7-x)/3, which of the following must be true?
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01 Apr 2016, 02:26
leeto wrote:
Bunuel, Sorry that bother you but, in my humble opinion, it seems that Chiragjordan is correct. II is not true.
A simple check can prove it :
From II we have that Case A: x > -1 OR Case B: x < -5
From Case A let's take x = 0
4<[(7-x)/3] => 4<[(7-0)/3] - is not true => Case A => is not working
Because problem's type is MUST BE not COULD BE => the answer is B ( only III MUST BE true ) .
Bunuel, please, could you confirm ?
This is an OG question and the answer is D. There are several solutions given on previous pages. Sorry but I don't have anything much to add...
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Re: If 4<(7-x)/3, which of the following must be true?
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01 Apr 2016, 02:33
Bunuel wrote: leeto wrote:
Bunuel, Sorry that bother you but, in my humble opinion, it seems that Chiragjordan is correct. II is not true.
A simple check can prove it :
From II we have that Case A: x > -1 OR Case B: x < -5
From Case A let's take x = 0
4<[(7-x)/3] => 4<[(7-0)/3] - is not true => Case A => is not working
Because problem's type is MUST BE not COULD BE => the answer is B ( only III MUST BE true ) .
Bunuel, please, could you confirm ?
This is an OG question and the answer is D. There are several solutions given on previous pages. Sorry but I don't have anything much to add... A. x=3 B. x^2=10 C. x<4 D. |x|=1 E. x>-10 Answer is E (x>-10), because as x=5 then it's more than -10. Or: If \(-1<x<10\), then which of the following must be true about \(x\):A. x=3 B. x^2=10 C. x<4 D. |x|=1 E. x<120 Again answer is E, because ANY \(x\) from \(-1<x<10\) will be less than 120 so it's always true about the number from this range to say that it's less than 120. Or: If \(-1<x<0\) or \(x>1\), then which of the following must be true about \(x\):A. x>1 B. x>-1 C. |x|<1 D. |x|=1 E. |x|^2>1 As \(-1<x<0\) or \(x>1\) then ANY \(x\) from these ranges would satisfy \(x>-1\). So B is always true. \(x\) could be for example -1/2, -3/4, or 10 but no matter what \(x\) actually is it's IN ANY CASE more than -1. So we can say about \(x\) that it's more than -1. On the other hand for example A is not always true as it says that \(x>1\), which is not always true as \(x\) could be -1/2 and -1/2 is not more than 1. Hope it's clear.
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Re: If 4<(7-x)/3, which of the following must be true?
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01 Apr 2016, 02:36
Bunuel wrote: Bunuel wrote: leeto wrote:
Bunuel, Sorry that bother you but, in my humble opinion, it seems that Chiragjordan is correct. II is not true.
A simple check can prove it :
From II we have that Case A: x > -1 OR Case B: x < -5
From Case A let's take x = 0
4<[(7-x)/3] => 4<[(7-0)/3] - is not true => Case A => is not working
Because problem's type is MUST BE not COULD BE => the answer is B ( only III MUST BE true ) .
Bunuel, please, could you confirm ?
This is an OG question and the answer is D. There are several solutions given on previous pages. Sorry but I don't have anything much to add... A. x=3 B. x^2=10 C. x<4 D. |x|=1 E. x>-10 Answer is E (x>-10), because as x=5 then it's more than -10. Or: If \(-1<x<10\), then which of the following must be true about \(x\):A. x=3 B. x^2=10 C. x<4 D. |x|=1 E. x<120 Again answer is E, because ANY \(x\) from \(-1<x<10\) will be less than 120 so it's always true about the number from this range to say that it's less than 120. Or: If \(-1<x<0\) or \(x>1\), then which of the following must be true about \(x\):A. x>1 B. x>-1 C. |x|<1 D. |x|=1 E. |x|^2>1 As \(-1<x<0\) or \(x>1\) then ANY \(x\) from these ranges would satisfy \(x>-1\). So B is always true. \(x\) could be for example -1/2, -3/4, or 10 but no matter what \(x\) actually is it's IN ANY CASE more than -1. So we can say about \(x\) that it's more than -1. On the other hand for example A is not always true as it says that \(x>1\), which is not always true as \(x\) could be -1/2 and -1/2 is not more than 1. Hope it's clear. Similar questions to practice: if-4x-12-x-9-which-of-the-following-must-be-true-101732.htmlif-it-is-true-that-x-2-and-x-7-which-of-the-following-m-129093.html
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Re: If 4<(7-x)/3, which of the following must be true?
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12 Apr 2016, 00:31
mn2010 wrote: If 4<(7-x)/3, which of the following must be true? I. 5<x II. |x+3|>2 III. -(x+5) is positive A) II only B) III only C) I and II only D) II and III only E) I, II and III I am confused about statement II ???? Simplify 4<(7-x)/3 and you get x < -5. Any of the statement says it would be true. (I) 5 < X i.e. X > 5 NOT true. (II) |x+3|>2 - range for this is -5 < X < 5. True. (III) -(x+5) i.e. -x-5 as x is less than -5 the values it would take will be -6, -7 and so on. in all these cases -(x+5) will be positive. True Hence D is the correct answer.
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Re: If 4<(7-x)/3, which of the following must be true?
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01 Nov 2016, 21:11
Bunuel wrote: mn2010 wrote: If 4<[(7-x)/3], which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive
A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III
I am not confused about statement II ???? Good question, +1. Note that we are asked to determine which MUST be true, not could be true. \(4<\frac{7-x}{3}\) --> \(12<7-x\) --> \(x<-5\). So we know that \(x<-5\), it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range \(x<-5\). Basically the question asks: if \(x<-5\) which of the following is true? I. \(5<x\) --> not true as \(x<-5\). II. \(|x+3|>2\), this inequality holds true for 2 cases, (for 2 ranges): 1. when \(x+3>2\), so when \(x>-1\) or 2. when \(-x-3>2\), so when \(x<-5\). We are given that second range is true (\(x<-5\)), so this inequality holds true. Or another way: ANY \(x\) from the range \(x<-5\) (-5.1, -6, -7, ...) will make \(|x+3|>2\) true, so as \(x<-5\), then \(|x+3|>2\) is always true. III. \(-(x+5)>0\) --> \(x<-5\) --> true. Answer: D. Hope it's clear. In II. |x+3|>2 If we have two cases where x>-1 and x<-5, then how can it MUST BE TRUE? Not 100% clear on this. Thanks for Looking into this. Sandeep
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Re: If 4<(7-x)/3, which of the following must be true?
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02 Jan 2017, 22:31
Bunuel wrote: mn2010 wrote: If 4<[(7-x)/3], which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive
A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III
I am not confused about statement II ???? Good question, +1. Note that we are asked to determine which MUST be true, not could be true. \(4<\frac{7-x}{3}\) --> \(12<7-x\) --> \(x<-5\). So we know that \(x<-5\), it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range \(x<-5\). Basically the question asks: if \(x<-5\) which of the following is true? I. \(5<x\) --> not true as \(x<-5\). II. \(|x+3|>2\), this inequality holds true for 2 cases, (for 2 ranges): 1. when \(x+3>2\), so when \(x>-1\) or 2. when \(-x-3>2\), so when \(x<-5\). We are given that second range is true (\(x<-5\)), so this inequality holds true. Or another way: ANY \(x\) from the range \(x<-5\) (-5.1, -6, -7, ...) will make \(|x+3|>2\) true, so as \(x<-5\), then \(|x+3|>2\) is always true. III. \(-(x+5)>0\) --> \(x<-5\) --> true. Answer: D. Hope it's clear. Regarding the option II shouldn't the condition x>-1 be satisfied ?
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Re: If 4<(7-x)/3, which of the following must be true?
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03 Jan 2017, 02:02
Animatzer wrote: Bunuel wrote: mn2010 wrote: If 4<[(7-x)/3], which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive
A) II only
B) III only
C) I and II only
D) II and III only
E) I, II and III
I am not confused about statement II ???? Good question, +1. Note that we are asked to determine which MUST be true, not could be true. \(4<\frac{7-x}{3}\) --> \(12<7-x\) --> \(x<-5\). So we know that \(x<-5\), it's given as a fact. Now, taking this info we should find out which of the following inequalities will be true OR which of the following inequalities will be true for the range \(x<-5\). Basically the question asks: if \(x<-5\) which of the following is true? I. \(5<x\) --> not true as \(x<-5\). II. \(|x+3|>2\), this inequality holds true for 2 cases, (for 2 ranges): 1. when \(x+3>2\), so when \(x>-1\) or 2. when \(-x-3>2\), so when \(x<-5\). We are given that second range is true (\(x<-5\)), so this inequality holds true. Or another way: ANY \(x\) from the range \(x<-5\) (-5.1, -6, -7, ...) will make \(|x+3|>2\) true, so as \(x<-5\), then \(|x+3|>2\) is always true. III. \(-(x+5)>0\) --> \(x<-5\) --> true. Answer: D. Hope it's clear. Regarding the option II shouldn't the condition x>-1 be satisfied ? Check here: if-4-7-x-3-which-of-the-following-must-be-true-99015.html#p853541
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Re: If 4<(7-x)/3, which of the following must be true?
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23 Mar 2017, 08:02
let's simpify from the beginning: 12<7-x
x<-5
let's test 1: doesn't work C,E out
let's test 2: |-6+3|>2 works fine
let's test 3: -(-6+5)= 1, hence, positive
Answer is D
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Re: If 4<(7-x)/3, which of the following must be true?
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05 Apr 2017, 10:24
mn2010 wrote: If 4<(7-x)/3, which of the following must be true? I. 5<x II. |x+3|>2 III. -(x+5) is positive A) II only B) III only C) I and II only D) II and III only E) I, II and III I am confused about statement II ???? Responding to a pm: Quote: In this question, I found that option two has two ranges. x > - or x < -5. So why this becomes sufficient? Don't we need only one clear answer to prove the sufficiency? If I have three ranges and one of them is good to prove the sufficiency, then also can we discard the other two?
You are given that x < -5. You obtain this because you are given that 4<(7-x)/3. So x can take values such as -5.4, -6, -100, -54637 etc Which of the following MUST BE TRUE? II. |x+3|>2 Gives x < -5 OR x > -1 For every value that x can take, is this statement true? Yes. For every value that x can take it is "'less than 5" or "more than -1". All our values are actually "less than -5". We need x to satisfy either "x < -5" or "x > -1".
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Re: If 4<(7-x)/3, which of the following must be true?
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29 May 2017, 22:50
mn2010 wrote: If 4<(7-x)/3, which of the following must be true? I. 5<x II. |x+3|>2 III. -(x+5) is positive A) II only B) III only C) I and II only D) II and III only E) I, II and III I am confused about statement II ???? _________________
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Re: If 4<(7-x)/3, which of the following must be true?
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29 May 2017, 22:50
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