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Set P consists of the first n positive multiples of 3 and set Q
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23 Mar 2019, 09:00
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Set P consists of the first n positive multiples of 3 and set Q consists of the first m positive multiples of 5. The sum of all the numbers in set P is equal to R and the sum of all the numbers in set Q is equal to S. If 'm 'and 'n' are positive integers, is the difference between R and S odd? I. m is odd and n is even II. m can be expressed in the form of 4x +3 and n can be expressed in the form of 2x, where x is a positive integer
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Set P consists of the first n positive multiples of 3 and set Q
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Updated on: 24 Mar 2019, 09:54
kiran120680 wrote: Set P consists of the first n positive multiples of 3 and set Q consists of the first m positive multiples of 5. The sum of all the numbers in set P is equal to R and the sum of all the numbers in set Q is equal to S. If 'm 'and 'n' are positive integers, is the difference between R and S odd?
I. m is odd and n is even II. m can be expressed in the form of 4x +3 and n can be expressed in the form of 2x, where x is a positive integer As it can be hard to understand what we're dealing with just by reading, we'll first break things down into bitesize chunks. This is a Precise approach. We know that R = 3 + 6 + 9 + ... for n multiples so R = 3(1 + 2 + 3... n), i.e. R is 3 * the sum of the first n numbers. Similarly, S = 5 * the sum of the first m numbers. Since R  S is odd only if both R,S are even or both are odd, we need to know if the sums 1+2+...n and 1+2+...m are even or odd. Using the standard arithmetic sum, 1+2+...n = n(n+1)/2 which is even if n or n+1 is a multiple of 4 and odd otherwise. Now that we know exactly what to look for, let's look at our statements. (1) does not tell us if (m or m+1) and (n or n+1) are multiples of 4. (2) tells us that m+1 is a multiple of 4 but does not tell us if n or n+1 are a multiple of 4. Combining gives us no information on whether n or n+1 is a multiple of 4. (E) is our answer.
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Re: Set P consists of the first n positive multiples of 3 and set Q
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24 Mar 2019, 09:40
DavidTutorexamPAL wrote: kiran120680 wrote: Set P consists of the first n positive multiples of 3 and set Q consists of the first m positive multiples of 5. The sum of all the numbers in set P is equal to R and the sum of all the numbers in set Q is equal to S. If 'm 'and 'n' are positive integers, is the difference between R and S odd?
I. m is odd and n is even II. m can be expressed in the form of 4x +3 and n can be expressed in the form of 2x, where x is a positive integer As it can be hard to understand what we're dealing with just by reading, we'll first break things down into bitesize chunks. This is a Precise approach. We know that P = 3 + 6 + 9 + ... for n multiples so P = 3(1 + 2 + 3... n), i.e. P is 3 * the sum of the first n numbers. Similarly, Q = 5 * the sum of the first m numbers. Since R  S is odd only if both R,S are even or both are odd, we need to know if the sums 1+2+...n and 1+2+...m are even or odd. Using the standard arithmetic sum, 1+2+...n = n(n+1)/2 which is even if n or n+1 is a multiple of 4 and odd otherwise. Now that we know exactly what to look for, let's look at our statements. (1) does not tell us if (m or m+1) and (n or n+1) are multiples of 4. (2) tells us that m+1 is a multiple of 4 but does not tell us if n or n+1 are a multiple of 4. Combining gives us no information on whether n or n+1 is a multiple of 4. (E) is our answer. Little confused, is there any better way to solve this question.



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Re: Set P consists of the first n positive multiples of 3 and set Q
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24 Mar 2019, 09:52
mangamma wrote: Little confused, is there any better way to solve this question.
Hey mangamma, The logic of this question is indeed hard. Try using numbers to make things concrete; this is a useful tool for approaching questions you don't really get. In this case: (1) trying m = 1 and n = 2 gives R = 3+6 = 9 and Q = 5. Then R  S = 9  5 which is even. trying m = 3 and n = 2 gives R = 9 and S = 5 + 10 + 15 = 30. Then R  S = 30 9 = 21 which is odd. Insufficient. (2) so we can still pick m = 3 and n = 2, giving RS odd. We'll keep m = 3 and change to n = 4, giving S =30 like before and R = 3+6+9+12 = 30. Then RS = 30  30 = 0 which is even. Insufficient. Combined: Both examples given in (2), i.e. (m,n)=(3,2) and (m,n)=(3,4) work when combining the statements as well. So still insufficient. Hence (E). Also, I had a typo in the original explanation which I have now fixed. Hope it is clearer
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Re: Set P consists of the first n positive multiples of 3 and set Q
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24 Mar 2019, 09:58
DavidTutorexamPAL wrote: mangamma wrote: Little confused, is there any better way to solve this question.
Hey mangamma, The logic of this question is indeed hard. Try using numbers to make things concrete; this is a useful tool for approaching questions you don't really get. In this case: (1) trying m = 1 and n = 2 gives R = 3+6 = 9 and Q = 5. Then R  S = 9  5 which is even. trying m = 3 and n = 2 gives R = 9 and S = 5 + 10 + 15 = 30. Then R  S = 30 9 = 21 which is odd. Insufficient. (2) so we can still pick m = 3 and n = 2, giving RS odd. We'll keep m = 3 and change to n = 4, giving S =30 like before and R = 3+6+9+12 = 30. Then RS = 30  30 = 0 which is even. Insufficient. Combined: Both examples given in (2), i.e. (m,n)=(3,2) and (m,n)=(3,4) work when combining the statements as well. So still insufficient. Hence (E). Also, I had a typo in the original explanation which I have now fixed. Hope it is clearer Now its claer. Thanks for the explanation.



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Re: Set P consists of the first n positive multiples of 3 and set Q
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24 Mar 2019, 10:14
DavidTutorexamPAL wrote: mangamma wrote: Little confused, is there any better way to solve this question.
Hey mangamma, The logic of this question is indeed hard. Try using numbers to make things concrete; this is a useful tool for approaching questions you don't really get. In this case: (1) trying m = 1 and n = 2 gives R = 3+6 = 9 and Q = 5. Then R  S = 9  5 which is even. trying m = 3 and n = 2 gives R = 9 and S = 5 + 10 + 15 = 30. Then R  S = 30 9 = 21 which is odd. Insufficient. (2) so we can still pick m = 3 and n = 2, giving RS odd. We'll keep m = 3 and change to n = 4, giving S =30 like before and R = 3+6+9+12 = 30. Then RS = 30  30 = 0 which is even. Insufficient. Combined: Both examples given in (2), i.e. (m,n)=(3,2) and (m,n)=(3,4) work when combining the statements as well. So still insufficient. Hence (E). Also, I had a typo in the original explanation which I have now fixed. Hope it is clearer I too little confused with the solution. Now I understood. Thank you David



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Set P consists of the first n positive multiples of 3 and set Q
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24 Mar 2019, 11:17
kiran120680 wrote: Set P consists of the first n positive multiples of 3 and set Q consists of the first m positive multiples of 5. The sum of all the numbers in set P is equal to R and the sum of all the numbers in set Q is equal to S. If 'm 'and 'n' are positive integers, is the difference between R and S odd?
I. m is odd and n is even II. m can be expressed in the form of 4x +3 and n can be expressed in the form of 2x, where x is a positive integer Here is how I solved. This is a Yes/No question and you need to find all the areas to see if you are getting consistent answers. By looking at the statements, I got an idea that while testing conditions, n has to be odd and m has to be even! So I took two examples so it'll be easy to test/solve: Example 1: P={3,6,9} => n=3 and ΣP=18=R & Q= {5,10} =>m=2 and ΣQ=15=S Nowhere in the questions it is mentioned that the multiples should be consecutive. So I'm gonna take different numbers now. Example 2: P={3,9,15} => n=3 and ΣP=27=R & Q= {10,15} =>m=2 and ΣQ=25=S Another hint: We gotta find if RS=odd. As per number property rules, oddeven=odd or evenodd=odd(keep this in kind while taking examples. It'll help!) Moving onto the statements Statement (1): m is odd and n is even Now the role of examples come in. From example 1, RS= 1815=3 ODD......YES example 2, RS= 2725=2 EVEN...........NO Different answers.....INSUFFICIENT Statement (2): m can be expressed in the form of 4x +3 and n can be expressed in the form of 2x m=4x+3=odd (odd+even=odd) and n=2x= even Now this statement is as same as statement 1 Different answers.....INSUFFICIENT Combining statement (1) + (2) would be same as above. Different answers. INSUFFICIENT Hence, answer is option E
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Set P consists of the first n positive multiples of 3 and set Q
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