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If [x] is the least integer greater than or equal to x, and [x/2]=3, w [#permalink]
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12 Jun 2017, 01:04
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If [x] is the least integer greater than or equal to x, and [x/2]=3, what is the scope of x？ A. 3<x≤4 B. 8<x≤9 C. 8<x≤10 D. 9<x≤12 E. 4<x≤6
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w [#permalink]
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12 Jun 2017, 03:40
MathRevolution wrote: If [x] is the least integer greater than or equal to x, and [x/2]=3, what is the scope of x？
A. 3<x≤4 B. 8<x≤9 C. 8<x≤10 D. 9<x≤12 E. 4<x≤6 [x/2]=3 maximum integer value for x could be 6. [6/2] = [3] = 3 substituting x = 5, we get = [5/2] = [2.5] = 3 substituting x = 4 , we get = [4/2] =[2] = 2 So x has to be greater than 4 and less than or equal to 6. Therefore scope of x = 4<x≤6. Answer E...



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Re: If [x] is the least integer greater than or equal to x, and [x/2]=3, w [#permalink]
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14 Jun 2017, 01:27
==> For [x], you get [1.2]=2, which means rounded up. In order to get [x/2]=3, you get 2<x/2≤3 and then 4<x≤6. Therefore, the answer is E. Answer: E
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w [#permalink]
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20 Jun 2017, 12:18
MathRevolution wrote: ==> For [x], you get [1.2]=2, which means rounded up.... @MathRevoltion, would you please explain how you derived this portion a little more?
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w [#permalink]
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30 Jun 2017, 10:42
genxer123 wrote: MathRevolution wrote: ==> For [x], you get [1.2]=2, which means rounded up.... @MathRevoltion, would you please explain how you derived this portion a little more? Hi genxer123, Its given [x] is the least integer greater than or equal to x. Therefore if we have 1.2; [1.2] will give least integer greater than or equal to 1.2 In this case 2 is the least integer greater than 1.2, hence [1.2] = 2 Hope its clear now.



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Re: If [x] is the least integer greater than or equal to x, and [x/2]=3, w [#permalink]
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14 Aug 2017, 18:46
sashiim20 wrote: MathRevolution wrote: If [x] is the least integer greater than or equal to x, and [x/2]=3, what is the scope of x？
A. 3<x≤4 B. 8<x≤9 C. 8<x≤10 D. 9<x≤12 E. 4<x≤6 [x/2]=3 maximum integer value for x could be 6. [6/2] = [3] = 3 substituting x = 5, we get = [5/2] = [2.5] = 3 substituting x = 4 , we get = [4/2] =[2] = 2 So x has to be greater than 4 and less than or equal to 6. Therefore scope of x = 4<x≤6. Answer E... Hello, Shashi I am not sure I am following your approach. Could you please help me understand by giving a different explanation?



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If [x] is the least integer greater than or equal to x, and [x/2]=3, w [#permalink]
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14 Aug 2017, 21:34
sashiim20 wrote: genxer123 wrote: MathRevolution wrote: ==> For [x], you get [1.2]=2, which means rounded up.... @MathRevoltion, would you please explain how you derived this portion a little more? Hi genxer123, Its given [x] is the least integer greater than or equal to x. Therefore if we have 1.2; [1.2] will give least integer greater than or equal to 1.2 In this case 2 is the least integer greater than 1.2, hence [1.2] = 2 Hope its clear now. sashiim20 , I missed your post! Belated thanks and kudos. As I reread, I see now that 1.2 was a random example of what [x] meant. I understood the rule. I just couldn't figure out from where the value 1.2 came. The sentence didn't say, "If we have a number such as 1.2," so I decided that I was missing something (namely, 1.2 in the calculations), and that I had simply guessed the right answer. I see now that the number chosen was an example. Cheers!
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If [x] is the least integer greater than or equal to x, and [x/2]=3, w [#permalink]
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14 Aug 2017, 23:34
Blackbox wrote: sashiim20 wrote: MathRevolution wrote: If [x] is the least integer greater than or equal to x, and [x/2]=3, what is the scope of x？
A. 3<x≤4 B. 8<x≤9 C. 8<x≤10 D. 9<x≤12 E. 4<x≤6 [x/2]=3 maximum integer value for x could be 6. [6/2] = [3] = 3 substituting x = 5, we get = [5/2] = [2.5] = 3 substituting x = 4 , we get = [4/2] =[2] = 2 So x has to be greater than 4 and less than or equal to 6. Therefore scope of x = 4<x≤6. Answer E... Hello, Shashi I am not sure I am following your approach. Could you please help me understand by giving a different explanation? Hi Blackbox, Question says [x] is the least integer greater than or equal to x. And [x/2]=3 So, maximum value of x when x/2 would be equal to 3 is 6. When x = 6, [6/2] = 3 Now when we take x = 5 , 5/2 = 2.5 Now its given [x] is least integer greater than or equal to x. Therefore for [2.5], least integer greater than or equal to 2.5 is = 3 Therefore x can have value of 6 and 5. Now when we take x = 4 , 4/2 = 2 Therefore for [2], least integer greater than or equal to 2 is = 2.  Which is not equal to 3 as given in the equation. Hence x cannot be 4. If we take x = 7, x/2 = 3.5. For [3.5] least integer greater than or equal to 3.5 is = 4  Which is not equal to 3 as given in the equation. Hence x cannot be 7. Therefore x has to be greater than 4 and less than or equal to 6. Given by x = 4<x≤6. Answer (E)... Hope its clear now...




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