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Re: If x is a positive integer, what is the remainder when x is divided by [#permalink]
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12 Oct 2017, 08:54
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tuanh135 wrote:
If x is a positive integer, what is the remainder when x is divided by 7?
(1) The remainder when x is divided by 4 is 3 (2) The remainder when x is divided by 5 is 1
Target question:What is the remainder when x is divided by 7?
Statement 1: The remainder when x is divided by 4 is 3 When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
So, if the remainder when x is divided by 4 is 3, then some possible values of x are: 3, 7, 11, 15, 19, 23, etc Let's examine some of these possible values of x Case a: If x = 3, then the remainder when x is divided by 7 is 3 Case b: If x = 7, then the remainder when x is divided by 7 is 0 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The remainder when x is divided by 5 is 1 Some possible values of x are: 1, 6, 11, 16, 21, 26, 31, etc Let's examine some of these possible values of x Case a: If x = 1, then the remainder when x is divided by 7 is 1 Case b: If x = 6, then the remainder when x is divided by 7 is 6 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that some possible values of x are: 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, etc Statement 2 tells us that some possible values of x are: 1, 6, 11, 16, 21, 26, 31, etc Since we already have 2 possible x-values that BOTH statements share, let's examine the following cases:
Case a: If x = 11, then the remainder when x is divided by 7 is 4 Case b: If x = 31, then the remainder when x is divided by 7 is 3 Since we still cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
If x is a positive integer, what is the remainder when x is divided by [#permalink]
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12 Oct 2017, 08:55
1
tuanh135 wrote:
If x is a positive integer, what is the remainder when x is divided by 7?
(1) The remainder when x is divided by 4 is 3 (2) The remainder when x is divided by 5 is 1
Statement 1: x=4k+3, where k is any integer. Thus there could be multiple value of x and hence multiple remainders when divided by 7. Insufficient
Statement 2: x=5q+1, where q is any integer. Thus there could be multiple value of x and hence multiple remainders when divided by 7. Insufficient
Combining 1 and 2 we know x is of the form 4k+3 & 5q+1, so x can be 11 or 51, for k=q=2 and k=12 & q=10. so again multiple remainders possible. Hence Insufficient
Re: If x is a positive integer, what is the remainder when x is divided by [#permalink]
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27 Nov 2017, 19:18
tuanh135 wrote:
If x is a positive integer, what is the remainder when x is divided by 7?
(1) The remainder when x is divided by 4 is 3 (2) The remainder when x is divided by 5 is 1
We need to determine the remainder of x/7.
Statement One Alone:
The remainder when x is divided by 4 is 3.
We see that x can be values such as 3, 7, 11, 15, 19, 23, 27, 31, etc.
However, using those values, we get various remainders when dividing by 7. For example, when 3 is divided by 7, the remainder is 3, but when 7 is divided by 7, the remainder is 0. Statement one alone is not sufficient to answer the question.
Statement Two Alone:
The remainder when x is divided by 5 is 1.
We see that x can be values such as 1, 6, 11, 16, 21, 26, 31, etc.
However, using those values, we get various remainders when dividing by 7. For example, when 1 is divided by 7, the remainder is 1, but when 6 is divided by 7, the remainder is 6. Statement two alone is not sufficient to answer the question.
Statements One and Two Together:
Using the two statements together, we see that x could be 11 or 31. When x = 11, the remainder is 4 when 11 is divided by 7. However, when x = 31, the remainder is 3 when 31 is divided by 7.
Answer: E
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Re: If x is a positive integer, what is the remainder when x is divided by [#permalink]
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04 May 2018, 09:12
Hi Both are same approach, it is the matter of presentation that differs. "If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. " Example to explain this: Here D is Divisor, R is Remainder let N when divided by 2 gives remainder as 1. then N can be 1, 2+1, 2*2+1, 3*2+1... N can be 1, 3, 5, 7... so on...
Grasp the concept, terminology doesn't matter much.
Let me know if my understanding is correct or flawed.
Here are three important things you need to know about remainders:
If N divided by D equals Q with remainder R, then N = DQ + R For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0
Here, Stmnt 1: x = 4a + 3 So x = 3, 7, 11, 15... Stmnt 2: x = 5b + 1 So x = 1, 6, 11, 16 ...
First number of both types is 11. Next such number will be 11 + 4*5 = 31. 11 divided by 7 will give remainder 4. 31 divided by 7 will give remainder 3 and so on...