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If P and Q are integers, is [m][fraction](10^{2P} + Q)/3[/fraction][/m
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20 Oct 2018, 10:04
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If P and Q are integers, is \(\frac{(10^{2P} + Q)}{3}\) an integer? (1) Q = 5 (2) P*Q is even GMATbuster's Weekly GMAT Quant Quiz #5 Ques No 2
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Re: If P and Q are integers, is [m][fraction](10^{2P} + Q)/3[/fraction][/m
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20 Oct 2018, 11:29
If P and Q are integers, is (102P+Q)/3 is an integer
an integer? (1) Q = 5 (2) P*Q is
Option A : Q= 5, so term is (10^2P +5)/3...now if we have P=0 or P be any integer >0, (10^2P +5)/3 will be an integer Illustration: if P=0, (1+5)/3 = 2 or if P=1, 100+5/3= 105/3= 35
but what if P is negative , if P=1 it becomes (1/100+ 5)/3, which is not an integer
hence A is not sufficient
Option B: P *Q is even which means P is even Q is even P is odd, Q is even P is even and Q is odd
so lets say 10^2+4/3= 104/3 , not an integer but 10^2+5= 35 an integer so B is not sufficient
Lets take both , Q=5 and P needs to be even if P>0, then expression is definitely an integer as we discussed in Option A explanation but if P becomes negative , lets take P= 2 so it becomes 1/10000 +5/3 which is not an integer...so even together cant solve the question
Hence E is the answer




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Re: If P and Q are integers, is [m][fraction](10^{2P} + Q)/3[/fraction][/m
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20 Oct 2018, 10:08
A: We don't need to know the value of P so statement 1 is sufficient. regardless the numerator will be 10...05 and the property for if a number is divisible by 3 is to add the digits. so 1+5 = 6, thus it is an integer
Statement 2 doesn't give us a value for Q so its insufficient



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Re: If P and Q are integers, is [m][fraction](10^{2P} + Q)/3[/fraction][/m
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20 Oct 2018, 10:11
Stat 1  P =0 Q = 5 Ans 2 P=1 Q=5 Ans 0.01+5 / 3 NS Stm 2 P*Q even  either P is even or Q is even  NS combined P is even but if its 2 then int and if 2 then not so answer is E
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Re: If P and Q are integers, is [m][fraction](10^{2P} + Q)/3[/fraction][/m
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20 Oct 2018, 10:12
A.
We are not worried about the value of P, only Q. The first provides value of Q for which answer can be confirmed Yes as per divisibility rule of 3. The second statement mentions the following: P is even, Q is even Or P is even, Q is odd Or P is odd, Q is even There are cases (q=5 or q=6) for which we get both confirmed Yes and No. Thus, not sufficient.



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Re: If P and Q are integers, is [m][fraction](10^{2P} + Q)/3[/fraction][/m
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Updated on: 20 Oct 2018, 12:00
Statement 1: Q = 5 > remainder = 2 When \(10^2p\) divided by 3 + if p= 0, \(10^2p\) leave remainder =0 + if p>0, always leaves remainder = 1 + if p<0, this fraction does not divisible by 3
> Insufficient
Statement 2:
PQ Even. It is undecided whether \(10^(2P)\) and Q is even or odd, this leave different remainders when The fraction is divided by 3
> Insufficient
Combine 2 statements, Q is 5 and PQ is even. This means P must be even.
From analysis in Statement 1 above , P is even and P>0 then we have > \(\frac{(10^(2P)+Q)}{3}\) is divisible by 3
—> Sufficient
Hence, Choice C
Originally posted by yenbh on 20 Oct 2018, 10:12.
Last edited by yenbh on 20 Oct 2018, 12:00, edited 2 times in total.



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Re: If P and Q are integers, is [m][fraction](10^{2P} + Q)/3[/fraction][/m
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20 Oct 2018, 13:39
A
To be divisible by 3, the sum of all the numbers should be divisible by 3
A)The sum of all the digits in the first number is 1 whatever be P.Also +5 implies 1+5=6 irrespective of whatever is P.SUFFICIENT.
B)P*Q is even.One case is p is even q is odd.Not always divisible by 3.INSUFFICIENT.




Re: If P and Q are integers, is [m][fraction](10^{2P} + Q)/3[/fraction][/m
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20 Oct 2018, 13:39






