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If x is an integer, is x between 27 and 54?
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13 Nov 2019, 00:54
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Competition Mode Question If x is an integer, is x between 27 and 54? (1) The remainder when x is divided by 7 is 2. (2) The remainder when x is divided by 3 is 2.
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Re: If x is an integer, is x between 27 and 54?
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13 Nov 2019, 01:15
If x is an integer, is x between 27 and 54?
(1) The remainder when x is divided by 7 is 2. > x = 7p + 2, for all integers p > Many values of x are possible > Insufficient
(2) The remainder when x is divided by 3 is 2. > x = 3q + 2, for all integers q > Many values of x are possible > Insufficient
Combining (1) & (2), x leaves remainder 2 when divided 7 & 3 LCM (7, 3) = 21 > x = 21m + 2 for all integers m > Possible values = {. . . ,40, 19, 2, 23, 44, 65 . . . .} > Insufficient
IMO Option E



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Re: If x is an integer, is x between 27 and 54?
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13 Nov 2019, 04:36
Quote: If x is an integer, is x between 27 and 54?
(1) The remainder when x is divided by 7 is 2. (2) The remainder when x is divided by 3 is 2. (1) The remainder when x is divided by 7 is 2. insufic\(x/7=m7+2:2,9,16,23,30,37,44…\) (2) The remainder when x is divided by 3 is 2. insufic\(x/3=n3+2:2,5,8,11,14,17,20,23,26,29,32,35,38,41,44,47…\) (1 & 2) insufic\(x=23,44…\) or, \(x=7m+2…x=3n+2…7m+2=3n+2…7m=3n\) \((m,n)=(3,7;6,14;9,21…):x=7(3)+2=23…x=(23,44,65…)\) Ans (E)



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Re: If x is an integer, is x between 27 and 54?
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13 Nov 2019, 06:56
If x is an integer, is x between 27 and 54? (1) The remainder when x is divided by 7 is 2. Taking any random value of x is possible. if x = 9, R[9/7] = 2; is 27 < x < 54 NO if x = 30, R[30/7] = 2; is 27 < x < 54 YES INSUFFICIENT. (2) The remainder when x is divided by 3 is 2. Again approaching in a similar manner. if x = 11, R[11/3] = 2; is 27 < x < 54 NO if x = 29, R[29/3] = 2; is 27 < x < 54 YES INSUFFICIENT. Together 1 and 2 LCM (3,7) = 21 So, values that results in a remainder = 2 are 2, 23, 44, 65 ... so on. Hence, both possibilities still exists. INSUFFICIENT. IMO Answer E.
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Re: If x is an integer, is x between 27 and 54?
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13 Nov 2019, 08:46
Statement 1:x can be in any form of x = 7i + 2, where i is any nonnegative integer.. We can have x = 9 or x = 37, insufficient. Statement2:Similar to above, we can have x in the form of x = 3i + 2, where i is any nonnegative integer. Then x can be 3, 5, or 32. Insufficient. Combined:Focus on x  2, we know x  2 has a factor of 7 from (1) and a factor of 3 from (2). Then (x2) must have a factor of 21. We can express x as x = 21*i + 2, where i is a nonnegative integer. So we can have x = 2, x = 23, x = 44, etc. Still insufficient. Ans: E
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Re: If x is an integer, is x between 27 and 54?
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13 Nov 2019, 09:07
If x is an integer, is x between 27 and 54?
(1) The remainder when x is divided by 7 is 2. —> insufficient: x can be 23 or 44 (2) The remainder when x is divided by 3 is 2.—> insufficient: x can be 23 or 44 Combining 1 & 2 also x can be 23 or 44 So the answer is E
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Re: If x is an integer, is x between 27 and 54?
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13 Nov 2019, 21:47
We are informed that x is an integer between 27 and 54. We are to determine x.
Statement 1: The remainder when x is divided by 7 is 2
Not sufficient. Because the following integers in the given range leave a remainder of 2 when divided by 7: 30, 37, 44, 51. This implies there is no unique value of x, hence insufficient.
Statement 2: The remainder when x is divided by 3 is 2. This is also insufficient. We have the following possibilities for x: 29, 32, 35, 38, 41, 44, 47, 51. Since we have more than one possible value of x, statement 2 is also insufficient.
1+2 combining 1 and 2 lead to 44 and 51. This is still insufficient. We are not able to narrow down to one answer choice. Both 44 and 51 satisfy the conditions in statements 1 and 2.
The answer is, therefore, option E.



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Re: If x is an integer, is x between 27 and 54?
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13 Nov 2019, 22:35
X is an integer between 27 and 54
Statement 1 the remainder when x/7=2 eg 9/7=2 no
Eg2 30/2= 2 yes
Statement 1 is insufficient
Statement 2 X/3=2
Eg 11/3=2 No
32/3=2. Yes
Combining both statements
23/7=2 and 23/3=2. No 44/7=2 and 44/3=2. Yes
Hence E both statements together are insufficient
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Re: If x is an integer, is x between 27 and 54?
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13 Nov 2019, 23:47
(1) The remainder when x is divided by 7 is 2.
Numbers are 9, 16,23, 30,37,44, 51,58, 65, etc
Insufficient
(2) The remainder when x is divided by 3 is 2.
Numbers are 5, 8, 11, 14, 17,20,23,26, etc
Insufficient
Both statements together.
23,44, and the list goes on.
Therefore Answer is E IMO.



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Re: If x is an integer, is x between 27 and 54?
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14 Nov 2019, 00:20
1 X= 7k+2 .... x can be 44 & 65 etc 2 x= 3k+2 ..... x can 44 & 65 etc This implies E is the correct answer
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Re: If x is an integer, is x between 27 and 54?
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14 Nov 2019, 06:47
Bunuel wrote: Competition Mode Question If x is an integer, is x between 27 and 54? (1) The remainder when x is divided by 7 is 2. (2) The remainder when x is divided by 3 is 2. #1 The remainder when x is divided by 7 is 2. we get both yes & no insufficient #2 again insufficient from 1&2 LCM= 21 again yes and no IMO E




Re: If x is an integer, is x between 27 and 54?
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14 Nov 2019, 06:47






