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If x is an integer, then how many values of x will satisfy the equatio
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Updated on: 20 Sep 2018, 07:58
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Different methods to solve absolute value equations and inequalities Exercise Question #2If x is an integer, then how many values of x will satisfy the equation x  10  6 = 4? Options Previous Question  Next Question To read the article: Different methods to solve absolute value equations and inequalities
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If x is an integer, then how many values of x will satisfy the equatio
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Updated on: 20 Sep 2018, 21:06
Solution Given:• We are given that x is an integer, and • We are also given an absolute value equation, x  10  6 = 4 To find:• We need to find the number of values of x, that satisfy the given equation Approach and Working: • As seen in the previous question, the first step is to substitute x  10 as t, which gives • Now, applying the definition of x, as learnt in the article, we can write t  6 = 4 as,
o t  6 = 4, if t ≥ 6
Implies, t = 10, which is greater than 6 Now, substituting back t as x  10, we get, x  10 = 10 This again gives two cases, Case 1: x – 10 = 10, if x ≥ 10 Implies, x = 20, which is greater than 10 Thus, x = 20, is a possible value of x Case 2: x – 10 = 10, if x < 10 Implies, x = 0, which is also a possible value
o And, t  6 = 4, if t < 6
Implies, t = 2, which is less than 6 Now, substituting back t as x  10, we get, x  10 = 2 This again gives two cases, Case 1: x – 10 = 2, if x ≥ 10 Implies, x = 12, which is greater than 10 Thus, x = 12, is a possible value of x Case 2: x – 10 = 2, if x < 10 Implies, x = 8, which is less than 10 Thus, x = 8, is also a possible value
• Thus, the only possible values of x that satisfy the given equation are 0, 8, 12 and 20. • Therefore, the number of possible values of x is 4.
Hence, the correct answer is option E. Answer: E
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If x is an integer, then how many values of x will satisfy the equatio
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Updated on: 20 Sep 2018, 08:05
My Approach: Ix10I will always be positive and in order for x106=4 to be true x10=2 or x10=10 x10=2 1. x10=2 x=12 2. x+10=2 x=8 > x=12 or x=8 x10=10 1. x10=20 x=20 2. x+10=10 x=0 Left with four values: 0,8,10,12 So Answer: E Please correct me if I am wrong!! Edited! Was wrong first time...
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Originally posted by T1101 on 13 Sep 2018, 10:36.
Last edited by T1101 on 20 Sep 2018, 08:05, edited 2 times in total.



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Re: If x is an integer, then how many values of x will satisfy the equatio
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Updated on: 14 Sep 2018, 04:41
EgmatQuantExpert wrote: Different methods to solve absolute value equations and inequalities Exercise Question #2If x is an integer, then how many values of x will satisfy the equation x  10  6 = 4? Options Previous Question  Next Question To read the article: Different methods to solve absolute value equations and inequalities Basically, here we have to find values of x for which x10 = 2,10. So, x = 0,8,12,20 Hence, E.
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Re: If x is an integer, then how many values of x will satisfy the equatio
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14 Sep 2018, 04:39
x={0,8,12,20} So isn't the answer E?
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Re: If x is an integer, then how many values of x will satisfy the equatio
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14 Sep 2018, 07:28
Answer would be 'E', 4 possible values of 'x' {0,8,12,20}.



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Re: If x is an integer, then how many values of x will satisfy the equatio
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20 Sep 2018, 07:45
EgmatQuantExpert wrote: Solution Given:• We are given that x is an integer, and • We are also given an absolute value equation, x  10  6 = 4 To find:• We need to find the number of values of x, that satisfy the given equation Approach and Working: • As seen in the previous question, the first step is to substitute x  10 as t, which gives • Now, applying the definition of x, as learnt in the article, we can write t  6 = 4 as,
o t  6 = 4, if t ≥ 6
Implies, t = 10, which is greater than 6 Now, substituting back t as x  10, we get, x  10 = 10 This again gives two cases, Case 1: x – 10 = 10, if x ≥ 10 Implies, x = 20, which is greater than 10 Thus, x = 20, is a possible value of x Case 2: x – 10 = 10, if x < 10 Implies, x = 0, which is not less than 10 Thus, x = 0, is not a possible value
o And, t  6 = 4, if t < 6
Implies, t = 2, which is less than 6 Now, substituting back t as x  10, we get, x  10 = 2 This again gives two cases, Case 1: x – 10 = 2, if x ≥ 10 Implies, x = 12, which is greater than 10 Thus, x = 12, is a possible value of x Case 2: x – 10 = 2, if x < 10 Implies, x = 8, which is less than 10 Thus, x = 8, is also a possible value
• Thus, the only possible values of x that satisfy the given equation are 8, 12 and 20. • Therefore, the number of possible values of x is 3.
Hence, the correct answer is option D. Answer: DHello Payal In solution mentioned by you: The case 2 of lx10l=10; there should be (x10)=10 if x<10 So x=0 if x<10. Which is a possible solution. So the answer should be E.



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Re: If x is an integer, then how many values of x will satisfy the equatio
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20 Sep 2018, 08:03
Hey HimoGMAT, mittu, rahul16singh28, T1101You all are correct. There was a typo error. We have corrected the solution. Regards
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Re: If x is an integer, then how many values of x will satisfy the equatio
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20 Sep 2018, 08:44
EgmatQuantExpert wrote: Hey HimoGMAT, mittu, rahul16singh28, T1101You all are correct. There was a typo error. We have corrected the solution. Regards You also might want to update the second last line, where it currently says the number of possible solutions is 3.



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Re: If x is an integer, then how many values of x will satisfy the equatio
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29 Sep 2018, 11:28
chetan2u this one too please




Re: If x is an integer, then how many values of x will satisfy the equatio
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29 Sep 2018, 11:28






