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If 2 < x <= 5, then which of the following MUST be true? [#permalink]
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06 Oct 2016, 10:53
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If \(2 < x \leq {5}\), then which of the following MUST be true? A) \(1 < x^2 < 16\) B) \(4 < x^2 \leq {25}\) C) \(0 \leq {x^2} \leq {16}\) D) \(0 < x^2 \leq {25}\) E) \(4 \leq {x^2} < 36\)
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Re: If 2 < x <= 5, then which of the following MUST be true? [#permalink]
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06 Oct 2016, 11:30
GMATPrepNow wrote: If 2 < x < 5, then which of the following MUST be true?
A) 1 < x² < 16 B) 4 < x² < 25 C) 0 < x² < 16 D) 0 < x² < 25 E) 4 < x² < 36
Kudos for every correct solution. Given: \(2 < x \leq {5}\) Value of \(x^2\) can range from 0 to 25. Only option E covers the above range Answer: E Alternate method: Put x = 5 > A and C can't be true Put x = 0 > B and D can't be true Choice E works for all x between 2 and 5. Answer: E



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If 2 < x <= 5, then which of the following MUST be true? [#permalink]
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Updated on: 30 Nov 2016, 14:41
s1d1 wrote: can anybody explain the answer? Vyshak's solutions are great. Let's examine his second approach. If 2 < x < 5, then it's possible that x = 5, in which case x² = 25 In other words, it's possible that x² = 25 When we check the answer choices, we see that... Answer choice A says that x² < 16. In other words, it says that x² cannot equal 25. ELIMINATE A Answer choice C says that x² < 16. In other words, it says that x² cannot equal 25. ELIMINATE C Also, if 2 < x < 5, then it's possible that x = 0, in which case x² = 0 In other words, it's possible that x² = 0 When we check the remaining answer choices, we see that... Answer choice B says that 4 < x². In other words, it says that x² cannot equal 0. ELIMINATE B Answer choice D says that 0 < x². In other words, it says that x² cannot equal 0. ELIMINATE D We're left with 1 answer choice...E Cheers, Brent
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Originally posted by GMATPrepNow on 06 Oct 2016, 12:50.
Last edited by GMATPrepNow on 30 Nov 2016, 14:41, edited 1 time in total.



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Re: If 2 < x <= 5, then which of the following MUST be true? [#permalink]
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19 Nov 2016, 08:25
GMATPrepNow wrote: s1d1 wrote: can anybody explain the answer? Vyshak's solutions are great. Let's examine his second approach. If 2 < x < 5, then it's possible that x = 5, in which case x² = 25 In other words, it's possible that x² = 25 When we check the answer choices, we see that... Answer choice A says that x² < 16. In other words, it says that x² cannot equal 25. ELIMINATE A Answer choice C says that x² < 16. In other words, it says that x² cannot equal 25. ELIMINATE C Also, if 2 < x < 5, then it's possible that x = 0, in which case x² = 0 In other words, it's possible that x² = 0 When we check the remaining answer choices, we see that... Answer choice B says that 4 < x². In other words, it says that x² cannot equal 0. ELIMINATE B Answer choice D says that 0 < x². In other words, it says that x² cannot equal 0. ELIMINATE D We're left with 1 answer choice...E Cheers, Brent Square of any number can never b negative, answer D is correct.



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Re: If 2 < x <= 5, then which of the following MUST be true? [#permalink]
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19 Nov 2016, 08:30
afarrukh786 wrote: GMATPrepNow wrote: s1d1 wrote: can anybody explain the answer? Vyshak's solutions are great. Let's examine his second approach. If 2 < x < 5, then it's possible that x = 5, in which case x² = 25 In other words, it's possible that x² = 25 When we check the answer choices, we see that... Answer choice A says that x² < 16. In other words, it says that x² cannot equal 25. ELIMINATE A Answer choice C says that x² < 16. In other words, it says that x² cannot equal 25. ELIMINATE C Also, if 2 < x < 5, then it's possible that x = 0, in which case x² = 0 In other words, it's possible that x² = 0 When we check the remaining answer choices, we see that... Answer choice B says that 4 < x². In other words, it says that x² cannot equal 0. ELIMINATE B Answer choice D says that 0 < x². In other words, it says that x² cannot equal 0. ELIMINATE D We're left with 1 answer choice...E Cheers, Brent Square of any number can never b negative, answer D is correct. From the stem x CAN be 0, and if it is, then D is wrong. The correct answer is E. Please reread the solutions above.
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Re: If 2 < x <= 5, then which of the following MUST be true? [#permalink]
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19 Nov 2016, 09:40
From the stem x CAN be 0, and if it is, then D is wrong. The correct answer is E. Please reread the solutions
D option does not say equal to zero, it says greater than zero, if you see option D, there is not a sign of equal to



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Re: If 2 < x <= 5, then which of the following MUST be true? [#permalink]
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19 Nov 2016, 10:11
I could agree with all of you and eliminate abcd but what about e square of any number cannot be negative so how is option e true. Can anyone tell why option E. Sent from my A1601 using GMAT Club Forum mobile app



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Re: If 2 < x <= 5, then which of the following MUST be true? [#permalink]
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19 Nov 2016, 10:53
ashishahujasham wrote: I could agree with all of you and eliminate abcd but what about e square of any number cannot be negative so how is option e true.
Can anyone tell why option E. This to me is a simple question that is complicated by GMAT trickery in the way the answer choices are presented. the smallest value for x^2 is 0, and 0 is always greater than 4, so option E still fulfills the demands of the question. It is always true that x^2 is greater than or equal to 4 because it is always greater than 4.



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Re: If 2 < x <= 5, then which of the following MUST be true? [#permalink]
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19 Nov 2016, 11:04
adamm412 wrote: ashishahujasham wrote: I could agree with all of you and eliminate abcd but what about e square of any number cannot be negative so how is option e true.
Can anyone tell why option E. This to me is a simple question that is complicated by GMAT trickery in the way the answer choices are presented. the smallest value for x^2 is 0, and 0 is always greater than 4, so option E still fulfills the demands of the question. It is always true that x^2 is greater than or equal to 4 because it is always greater than 4. How can E be answer while it include negative numbers and zero also



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Re: If 2 < x <= 5, then which of the following MUST be true? [#permalink]
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19 Nov 2016, 11:13
afarrukh786 wrote: adamm412 wrote: ashishahujasham wrote: I could agree with all of you and eliminate abcd but what about e square of any number cannot be negative so how is option e true.
Can anyone tell why option E. This to me is a simple question that is complicated by GMAT trickery in the way the answer choices are presented. the smallest value for x^2 is 0, and 0 is always greater than 4, so option E still fulfills the demands of the question. It is always true that x^2 is greater than or equal to 4 because it is always greater than 4. How can E be answer while it include negative numbers and zero also Again it comes down to the way the question is presented: "which of the following MUST be true". In theory, answer E could have been 1,000,000 ≤ x^2 < 1,000,000 and it would still be the only correct answer because it is the only solution offered that contains the actual possible values of x^2. notice the maximum value of x^2 is 25 but answer E allows for up to 36... we know x^2 cannot get that big, but the way the solution is presented means x^2 never actually needs to reach ~36 in order for it to still satisfy those constraints. This is the same idea on the negative lower bound of x^2. Also, x^2 = 0 is a possible solution if x=0.



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Re: If 2 < x <= 5, then which of the following MUST be true? [#permalink]
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20 Nov 2016, 01:54
GMATPrepNow wrote: If \(2 < x \leq {5}\), then which of the following MUST be true?
A) \(1 < x^2 < 16\) B) \(4 < x^2 \leq {25}\) C) \(0 \leq {x^2} \leq {16}\) D) \(0 < x^2 \leq {25}\) E) \(4 \leq {x^2} < 36\)
Kudos for every correct solution. Ok lets make it simpler. Given is \(2 < x \leq {5}\) which means x can have the following values 1, 0, 1, 2, 3, 4, 5 (for simplification purpose i'm using integers. x can have a decimal values also as question doesn't say x is an integer) now see what all values can x^2 take. x^2 can take 0, 1, 4, 9, 16, 25. Yes? with this knowledge approach the answer choice. Only option E gives you all the above values of x^2.



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Re: If 2 < x <= 5, then which of the following MUST be true? [#permalink]
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20 Nov 2016, 03:28
afarrukh786 wrote: adamm412 wrote: ashishahujasham wrote: I could agree with all of you and eliminate abcd but what about e square of any number cannot be negative so how is option e true.
Can anyone tell why option E. This to me is a simple question that is complicated by GMAT trickery in the way the answer choices are presented. the smallest value for x^2 is 0, and 0 is always greater than 4, so option E still fulfills the demands of the question. It is always true that x^2 is greater than or equal to 4 because it is always greater than 4. How can E be answer while it include negative numbers and zero also I think you don't understand the logic of the question. The question asks: if \(2 < x \leq {5}\), then which of the following MUST be true? So, we KNOW that \(2 < x \leq {5}\) and should evaluate which of the options must be correct. If \(2 < x \leq {5}\), then only E must be true.
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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 2 < x <= 5, then which of the following MUST be true? [#permalink]
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20 Nov 2016, 05:09
GMATPrepNow wrote: If \(2 < x \leq {5}\), then which of the following MUST be true?
A) \(1 < x^2 < 16\)
B) \(4 < x^2 \leq {25}\)
C) \(0 \leq {x^2} \leq {16}\)
D) \(0 < x^2 \leq {25}\)
E) \(4 \leq {x^2} < 36\) Hi, No calculations required, just logic on the choices given... E has the widest range and contains ALL other choices, so if any of A to D is correct, E has to be correct.... But can we have TWO answers, No.. So E is the answer
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Re: If 2 < x <= 5, then which of the following MUST be true? [#permalink]
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20 Nov 2016, 06:35
GMATPrepNow wrote: If \(2 < x \leq {5}\), then which of the following MUST be true?
A) \(1 < x^2 < 16\)
B) \(4 < x^2 \leq {25}\)
C) \(0 \leq {x^2} \leq {16}\)
D) \(0 < x^2 \leq {25}\)
E) \(4 \leq {x^2} < 36\) Many students will assume that E is incorrect, because x² CANNOT equal 4. However, answer choice E does not suggest that x² can equal 4, it only states that x² must be GREATER THAN or equal to 4. Here's a similar example: If Joe has more than 5 shirts, which of the following can we conclude with certainty? A) Joe owns more than 6 shirts. NO. We can't conclude this, because it's possible that Joe owns exactly 6 shirts, and 6 is not greater than 6. B) Joe owns more than 3 shirts. YES. If Joe owns more than 5 shirts, then he definitely owns more than 3 shirts? Does this mean that Joe COULD own 2 shirts? No. If just means that we can be certain that he owns more than 3 shirts. Does that help? Cheers, Brent
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