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705-805 Level|   Arithmetic|      
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AmoyV
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x is a positive integer less than 20. What is the value of x? Updated on: 03 Sep 2014, 18:09
Originally posted by AmoyV on 03 Sep 2014, 16:26.
Last edited by Bunuel on 03 Sep 2014, 18:09, edited 1 time in total.
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x is a positive integer less than 20. What is the value of x?

(1) x is the sum of two consecutive integers.
(2) x is the sum of five consecutive integers.
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Bunuel
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x is a positive integer less than 20. What is the value of x? 03 Sep 2014, 18:15
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x is a positive integer less than 20. What is the value of x?

(1) x is the sum of two consecutive integers. Well, this one is clearly insufficient. For example, x could be 0 + 1 = 1 or 1 + 2 = 3. Not sufficient.

(2) x is the sum of five consecutive integers. Also, insufficient. For example, x could be 0 + 1 + 2 + 3 + 4 = 10 or 1 + 2 + 3 + 4 +5 = 15. Not sufficient.

(1)+(2) The same here: x could be 1 + 2 + 3 + 4 + 5 = 7 + 8 = 15 or -1 + 0 + 1 + 2 + 3 = 2 + 3 = 5. Not sufficient.

Answer: E.
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x is a positive integer less than 20. What is the value of x? 08 Dec 2014, 14:38
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small question:
does'nt statement 1 and 2 contradict each other in this question? isit possible in Gmat?
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x is a positive integer less than 20. What is the value of x? 08 Dec 2014, 14:48
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santorasantu
small question:
does'nt statement 1 and 2 contradict each other in this question? isit possible in Gmat?

On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

But , for this question, the statements, do not contradict. x could be 15, so the sum of 5 consecutive integers (1 + 2 + 3 + 4 + 5 = 15) and the sum of 2 consecutive integers (7 + 8 = 15). It can also be 5, again 5 is the the sum of 5 consecutive integers (-1 + 0 + 1 + 2 + 3 = 5) as well as the sum of 2 consecutive integers (2 + 3 = 5).


Hope it's clear.
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x is a positive integer less than 20. What is the value of x? 08 Dec 2014, 15:11
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Does the statement x is a positive integer mean that x can be 0?
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x is a positive integer less than 20. What is the value of x? 08 Dec 2014, 15:22
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Does the statement x is a positive integer mean that x can be 0?

0 is neither positive nor negative integer, so x cannot be 0.
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x is a positive integer less than 20. What is the value of x? 09 Dec 2014, 05:19
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Bunuel
santorasantu
small question:
does'nt statement 1 and 2 contradict each other in this question? isit possible in Gmat?

On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

But , for this question, the statements, do not contradict. x could be 15, so the sum of 5 consecutive integers (1 + 2 + 3 + 4 + 5 = 15) and the sum of 2 consecutive integers (7 + 8 = 15). It can also be 5, again 5 is the the sum of 5 consecutive integers (-1 + 0 + 1 + 2 + 3 = 5) as well as the sum of 2 consecutive integers (2 + 3 = 5).


Hope it's clear.


Thanks a lot for the clarification and also the explanation :idea:
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x is a positive integer less than 20. What is the value of x? 29 Oct 2016, 14:16
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Statement 1:

x can be 1,3,5,7,9,11,13,15,17,19

Insufficient

Statement 2:

x can be 5, 10, 15

Insufficient

Statement 1&2:

x can be 5 or 15.

Insufficient

E


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x is a positive integer less than 20. What is the value of x? 26 Oct 2017, 01:36
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St 1: x is the sum of two consecutive integers --> can be a+2, a+3 or a, a+1. So x will change, as we don't know the order of the consecutive numbers

St 2: X is sum of 5 consecutive integers --> can be a+5, a+6, a+7, a+8, a+9 or a+12, a+13..a+17. Again x will change. we don't know the order of consecutive numbers

1) 2) => no clarity on the value of consecutive numbers. hence E.
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x is a positive integer less than 20. What is the value of x? 06 Jun 2025, 04:08
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I have a doubt. It clearly says that x is a positive integer, so how can we take the value of X as 0 or -1...
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x is a positive integer less than 20. What is the value of x? Updated on: 06 Jun 2025, 06:21
Originally posted by Bunuel on 06 Jun 2025, 06:21.
Last edited by Bunuel on 06 Jun 2025, 06:21, edited 1 time in total.
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Bunuel
x is a positive integer less than 20. What is the value of x?

(1) x is the sum of two consecutive integers. Well, this one is clearly insufficient. For example, x could be 0 + 1 = 1 or 1 + 2 = 3. Not sufficient.

(2) x is the sum of five consecutive integers. Also, insufficient. For example, x could be 0 + 1 + 2 + 3 + 4 = 10 or 1 + 2 + 3 + 4 +5 = 15. Not sufficient.

(1)+(2) The same here: x could be 1 + 2 + 3 + 4 + 5 = 7 + 8 = 15 or -1 + 0 + 1 + 2 + 3 = 2 + 3 = 5. Not sufficient.

Answer: E.

I have a doubt. It clearly says that x is a positive integer, so how can we take the value of X as 0 or -1...


It says x is a positive integer, not that the numbers being added must be positive. So using numbers like -1 or 0 in the sum is fine, as long as the final result, x, is a positive integer.
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