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Joined: 02 Sep 2009
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Math Expert
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16 Sep 2014, 00:59
Official Solution: Question asks: is \(2*x*5*y=even\)? Now, since there is 2 as a multiple, then this expression will be even if \(5xy=integer\). Basically we are asked: is \(5xy=integer\)? Notice that \(x\) and \(y\) may not be integers for \(2*x*5*y\) to be even (example \(x=\frac{7}{9}\) and \(y=\frac{9}{7}\)) BUT if they are integers then \(2*x*5*y\) is even. (1) \(2 + x + 5 + y\) is an even integer. Given: \(2+x+5+y=even\). So, \(7+x+y=even\), which means that \(x+y=odd\). Not sufficient. (Consider \(x=1\) and \(y=2\) for an YES answer and \(x=1.3\) and \(y=1.7\) for a NO answer). (2) \(xy\) is an odd integer. Given: \(xy=odd\). Not sufficient. (Consider \(x=1\) and \(y=2\) for an YES answer and \(x=1.3\) and \(y=0.3\) for a NO answer). (1)+(2) Sum (1) and (2) \((x+y)+(xy)=odd_1+odd_2\), so \(2x=even\). This implies that \(x=integer\) and therefore \(y=integer\). Hence sufficient. Answer: C
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Re: M1618
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18 Mar 2016, 03:37
Hi,
Hope zero can be considered rite?
If its taken, then the answer is E. Kindly debrief?



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Re: M1618
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18 Mar 2016, 03:57



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Re M1618
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27 Aug 2016, 05:43
I think this is a highquality question and I agree with explanation.



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Re: M1618
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21 Nov 2016, 08:22
Great Question Here we need to see if 10xy is even or not Let P=10xy Note => If x and y are integers => 10xy will be always even irrespective of the value of x and y Lets look at statements Statement 1 x+y+7=even hence x+y=odd hmm x=1,y=2 => P = even x=1.2,y=1.8 => P = 18*12/10 => not an integer(we don't have to perform the division here, as 5 is in the denominator and no 5 is in the numerator => This wont be an integer) Hence not sufficient Statement 2 xy=odd hmm x=10,y=1=> P will be even if x=10.1,y=1.1 => p will not be an integer. Hence not sufficient Combining the two statements x+y=odd xy=odd adding them up 2x=odd+odd = even hence x => integer now y=oddx=> integer too Hence x and y are both integers hence P will always be even Hence C
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07 Jul 2017, 03:31
amazing questions



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21 Nov 2017, 13:39
(1)+(2) Sum (1) and (2) (x+y)+(x−y)=odd1+odd2(x+y)+(x−y)=odd1+odd2, so 2x=even2x=even. This implies that x=integerx=integer and therefore y=integery=integer. Hence sufficient.
Can someone explain how 2x= even implies , X is an integer



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21 Nov 2017, 21:08



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08 Jan 2018, 00:28
Hey Bunuel, Can you explain how "2x= even" implies , X is an integer When x = 1.6, 2*1.6 = 3.2 which is an even number. When x = 2, 2*2 = 4 which is an even number. Therefore x may or may not be an integer. Hence, the answer should be E  BOTH STATEMENTS ARE INSUFFICIENT



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08 Jan 2018, 00:36
rogueassasin wrote: Hey Bunuel, Can you explain how "2x= even" implies , X is an integer When x = 1.6, 2*1.6 = 3.2 which is an even number. When x = 2, 2*2 = 4 which is an even number. Therefore x may or may not be an integer. Hence, the answer should be E  BOTH STATEMENTS ARE INSUFFICIENT 3.2 is NOT an even number. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. So, ..., 4, 2, 0, 2, 4, ... are all even integers. An odd number is an integer that is not evenly divisible by 2. So, ..., 3, 1, 1, 3, 5, ... are all odd integers. For more check here: ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative MegathreadHope it helps.
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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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23 Jul 2018, 01:33
BunuelCan you please provide some methods of determining x is an integer/y is an integer in such questions? While I'm pretty confident about the even/odd bit  the number and integer type of question (not the concept, but the proving/establishing) is something I've come across for the first time. Thank you in advance!










