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If x+1 = b, where b is a nonzero integer, which of the following s [#permalink]
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07 Jan 2015, 21:09
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If x+1 = b, where b is a nonzero integer, which of the following statements must be true? I. b < 0 II. x < b III. x > b A. I only B. II only C. III only D. I and II only E. I and III only Source: eGMAT
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Re: If x+1 = b, where b is a nonzero integer, which of the following s [#permalink]
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07 Jan 2015, 21:37
hubahuba wrote: If x+1 = b, where b is a nonzero integer, which of the following statements must be true? I. b < 0 II. x < b III. x > b A. I only B. II only C. III only D. I and II only E. I and III only Source: eGMATI got this question on eGMAT and am looking for a more efficient method to solve such questions. x+1 = b x+1 = b Note that absolute value can never be negative and we know that b is not 0 so b must be positive. This means b must be negative. I must be true. For the others, use number line approach. _______________(1)_______0______________________________ b is the distance of x from 1. If x is on the left of 1, it will be negative and since b is positive, x < b. If x is to the right of 0, b will still be 1 greater than x. Say x = 5, then b = 6 (distance of 5 from 1). Hence x < b. II will always hold. III is not necessary. If x is say 2, b = 1 so b = 1. Here x < b. Answer (D)
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Re: If x+1 = b, where b is a nonzero integer, which of the following s [#permalink]
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08 Jan 2015, 02:44
VeritasPrepKarishma wrote: hubahuba wrote: If x+1 = b, where b is a nonzero integer, which of the following statements must be true? I. b < 0 II. x < b III. x > b A. I only B. II only C. III only D. I and II only E. I and III only Source: eGMATI got this question on eGMAT and am looking for a more efficient method to solve such questions. x+1 = b x+1 = b Note that absolute value can never be negative and we know that b is not 0 so b must be positive. This means b must be negative. I must be true. For the others, use number line approach. _______________(1)_______0______________________________ b is the distance of x from 1. If x is on the left of 1, it will be negative and since b is positive, x < b. If x is to the right of 0, b will still be 1 greater than x. Say x = 5, then b = 6 (distance of 5 from 1). Hence x < b. II will always hold. III is not necessary. If x is say 2, b = 1 so b = 1. Here x < b. Answer (D) Hi I am little confused. I tried with the typical method. Given that x+1 = b x+1 = b....... hence b is a negative number, and b is positive.. so I is true. Next.. x+1...then x+1 = b ...or..... (x+1) = b When X+1 = b x = b1 as b is positive, x < b When (X+1) = b x+1 = b x = b1 and then confusion.. can you please help..!!



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Re: If x+1 = b, where b is a nonzero integer, which of the following s [#permalink]
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08 Jan 2015, 07:09
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gauriranjekar wrote: VeritasPrepKarishma wrote: hubahuba wrote: If x+1 = b, where b is a nonzero integer, which of the following statements must be true? I. b < 0 II. x < b III. x > b A. I only B. II only C. III only D. I and II only E. I and III only Source: eGMATI got this question on eGMAT and am looking for a more efficient method to solve such questions. x+1 = b x+1 = b Note that absolute value can never be negative and we know that b is not 0 so b must be positive. This means b must be negative. I must be true. For the others, use number line approach. _______________(1)_______0______________________________ b is the distance of x from 1. If x is on the left of 1, it will be negative and since b is positive, x < b. If x is to the right of 0, b will still be 1 greater than x. Say x = 5, then b = 6 (distance of 5 from 1). Hence x < b. II will always hold. III is not necessary. If x is say 2, b = 1 so b = 1. Here x < b. Answer (D) Hi I am little confused. I tried with the typical method. Given that x+1 = b x+1 = b....... hence b is a negative number, and b is positive.. so I is true. Next.. x+1...then x+1 = b ...or..... (x+1) = b When X+1 = b x = b1 as b is positive, x < b When (X+1) = b x+1 = b x = b1 and then confusion.. can you please help..!! x+1 = b > b >=0 > b <= 0. Since we are given that b is a nonzero integer, then b is a negative integer: 1, 2, 3, ... x+1 = x+1, when x+1 > 0, so when x > 1. In this case x+1 = b > x = b  1. When b = 1, x = 0; when b = 2, then x = 1, ... > x < b. x+1 = (x+1), when x+1 <= 0, so when x <= 1. In this case (x+1) = b > x = b  1. When b = 1, x = 2; when b = 2, then x = 3, ... > x < b.
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Re: If x+1 = b, where b is a nonzero integer, which of the following s [#permalink]
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08 Jan 2015, 20:46
gauriranjekar wrote: VeritasPrepKarishma wrote: hubahuba wrote: If x+1 = b, where b is a nonzero integer, which of the following statements must be true? I. b < 0 II. x < b III. x > b A. I only B. II only C. III only D. I and II only E. I and III only Source: eGMATI got this question on eGMAT and am looking for a more efficient method to solve such questions. x+1 = b x+1 = b Note that absolute value can never be negative and we know that b is not 0 so b must be positive. This means b must be negative. I must be true. For the others, use number line approach. _______________(1)_______0______________________________ b is the distance of x from 1. If x is on the left of 1, it will be negative and since b is positive, x < b. If x is to the right of 0, b will still be 1 greater than x. Say x = 5, then b = 6 (distance of 5 from 1). Hence x < b. II will always hold. III is not necessary. If x is say 2, b = 1 so b = 1. Here x < b. Answer (D) Hi I am little confused. I tried with the typical method. Given that x+1 = b x+1 = b....... hence b is a negative number, and b is positive.. so I is true. Next.. x+1...then x+1 = b ...or..... (x+1) = b When X+1 = b x = b1 as b is positive, x < b When (X+1) = b x+1 = b x = b1 and then confusion.. can you please help..!! Bunuel has already solved your doubt so I will not provide the solution again but here is a link which tells you why it is very important to consider the range when you convert absolute value equation to a regular equation. i.e. when you substitute x+1 in place of x+1, it is very important to note that this is true only when x > 1. http://www.veritasprep.com/blog/2014/06 ... thegmat/
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If x+1 = b, where b is a nonzero integer, which of the following s [#permalink]
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09 Jan 2015, 06:25
Thank you for sharing the link.. it is quite helpful thanks Bunuel for the solution..!!



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Re: If x+1 = b, where b is a nonzero integer, which of the following s [#permalink]
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10 Mar 2016, 02:31
VeritasPrepKarishma wrote: If x is to the right of 0, b will still be 1 greater than x. Say x = 5, then b = 6 (distance of 5 from 1). Hence x < b. II will always hold.
Hi, I thought the second case should be If x is to the right of 1, since x can be zero and b=1. What am I missing?



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Re: If x+1 = b, where b is a nonzero integer, which of the following s [#permalink]
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05 Nov 2016, 19:44
If x+1 = b, where b is a nonzero integer, which of the following statements must be true? I. b < 0 II. x < b III. x > b Solution: If x+1 = b then b is equal to a negative value of an absolute value. So, b < 0. Secondly, If x+1 = a negative value, then (x+1) < 0. So, x < 1. So, both x and b are negative values. But magnitude of (x+1) equal to b. So x is one more negative than b. Example: If x = 5, then b = 4. Therefore, x < b. Lastly, x > b can't be true, because both the numbers have negative values. The negative value of x is more negative than that of b. So, the answer is D. Thanks in advance for the Kudos!!!



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Re: If x+1 = b, where b is a nonzero integer, which of the following s [#permalink]
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07 Nov 2016, 02:53
hubahuba wrote: If x+1 = b, where b is a nonzero integer, which of the following statements must be true? I. b < 0 II. x < b III. x > b A. I only B. II only C. III only D. I and II only E. I and III only Source: eGMATِAnother approach is plug in numbers but we need carefully to choose different numbers. From the prompt b is nonzero integer so X does not equal to 1. I will choose two values above and lower than 1. x>1.....choose x=1.......... b=2 x,1 .....choose x=2.............b=1 From above let's examine each statement I. b < 0...... from above examples. it is evident that b<0 for all ranges. Eliminate B & C II. x < b .....from above examples 1< 2 & 2<1 .. it is always correct. Eliminate A & E Answer :D



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Re: If x+1 = b, where b is a nonzero integer, which of the following s [#permalink]
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08 Dec 2017, 13:11
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Re: If x+1 = b, where b is a nonzero integer, which of the following s
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