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In this question, wouldn't statements 1 and 2 together be insufficient?
Question:
Is x² - y² divisible by 8?
1. x and y are even integers
2. x + y is divisible by 8
According to the answer key, the correct answer is C, but aren't the statements together insufficient? Consider:
The answer is yes if, for example x=6 and y=2 because (6+2)(6-2) is divisible by 8
The answer is no if x=4 and y=4 because (4+4)(4-4) is not divisible by 8
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Re: m15 question 23 [#permalink]
 11 Apr 2011, 11:59
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Fk5000 wrote: In this question, wouldn't statements 1 and 2 together be insufficient?
Question:
Is x² - y² divisible by 8?
1. x and y are even integers
2. x + y is divisible by 8
According to the answer key, the correct answer is C, but aren't the statements together insufficient? Consider:
The answer is yes if, for example x=6 and y=2 because (6+2)(6-2) is divisible by 8
The answer is no if x=4 and y=4 because (4+4)(4-4) is not divisible by 8 Infamous "0" is a multiple of everything "Or" 0 is divisible by everything but itself "Or" every known number is a factor of "0". Thus, 0 is divisible by 8. 0 when divided by 8 leaves a remainder 0. "0/8=0"
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Re: m15 question 23 [#permalink]
12 Apr 2011, 09:46
Fk5000 wrote: In this question, wouldn't statements 1 and 2 together be insufficient?
Question:
Is x² - y² divisible by 8?
1. x and y are even integers
2. x + y is divisible by 8
According to the answer key, the correct answer is C, but aren't the statements together insufficient? Consider:
The answer is yes if, for example x=6 and y=2 because (6+2)(6-2) is divisible by 8
The answer is no if x=4 and y=4 because (4+4)(4-4) is not divisible by 8 Hi Fluke, If it was mentioned in the question itself that x and y are integers (not necessarily even integers), Option B would have sufficed right?
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Re: m15 question 23 [#permalink]
12 Apr 2011, 12:45
fluke wrote: Fk5000 wrote: In this question, wouldn't statements 1 and 2 together be insufficient?
Question:
Is x² - y² divisible by 8?
1. x and y are even integers
2. x + y is divisible by 8
According to the answer key, the correct answer is C, but aren't the statements together insufficient? Consider:
The answer is yes if, for example x=6 and y=2 because (6+2)(6-2) is divisible by 8
The answer is no if x=4 and y=4 because (4+4)(4-4) is not divisible by 8 Infamous "0" is a multiple of everything "Or" 0 is divisible by everything but itself "Or" every known number is a factor of "0". Thus, 0 is divisible by 8. 0 when divided by 8 leaves a remainder 0. "0/8=0" Still Didn't get you fluke isn't statement 2 sufficient as x² - y²=(x+y)(x-y) now if (x+y) is divisible by 8 then whole term x² - y² will also be divisible by 8 did not understand how st 1 is useful
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Re: m15 question 23 [#permalink]
12 Apr 2011, 12:58
@ Warlock007, We are not told that x and y are integers. If x=3/4 and y= 3/2, statement B alone will not suffice. We need to be sure that x and y are integers. Thats what statement 1 tells us and thats how it is useful
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Re: m15 question 23 [#permalink]
12 Apr 2011, 13:23
Warlock007 wrote: Still Didn't get you fluke
isn't statement 2 sufficient
as x² - y²=(x+y)(x-y)
now if (x+y) is divisible by 8 then whole term x² - y² will also be divisible by 8
did not understand how st 1 is useful I agree with gmatpapa. x=6.8 y=1.2 x+y=6.8+1.2=8 x-y=6.8-1.2=5.6 x^2-y^2=(x+y)(x-y)=8*5.6=44.8 44.8 is not divisible by 8 44.8/8 = 448/80=28/5 will leave a remainder of 3. If both x and y were even integers, then x+y=even integer, x-y=even integer And (x+y) is divisible by 8, then (x+y)/8= integer \frac{x^2-y^2}{8}=\frac{(x+y)(x-y)}{8}\frac{x+y}{8}*(x-y)=integer*integer=integerThus 8 will divide x^2-y^2 leaving an integer as quotient and no remainder. Ans: "C" ************* Raise concern, if any.
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Re: m15 question 23 [#permalink]
12 Apr 2011, 14:05
I think Is x² - y² divisible by 8?
can be rephrased as Is (x-y)(x+y) divisible by 8 where x and y are integers. Is this correct?
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Re: m15 question 23 [#permalink]
12 Apr 2011, 14:09
gmat1220 wrote: I think Is x² - y² divisible by 8?
can be rephrased as Is (x-y)(x+y) divisible by 8 where x and y are integers. Is this correct? Why did you add the extra bit "where x and y are integers". I am not able to gather your thought process. I would just rephrase it as, "Is (x-y)(x+y) divisible by 8?".
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Re: m15 question 23 [#permalink]
12 Apr 2011, 21:51
Hello fluke
Is x² - y² divisible by 8?
I think the necessary condition (x+y)or(x-y) or their product divisible by 8 is not sufficient to answer the question. We also need the condition - Is x and y integers? to conclusively answer.
yes to both questions - the answer is yes
yes and no to questions - the answer is no
no and no to questions - the answer is no
I meant we need answers to two questions to answer this question - Is x² - y² divisible by 8? Isnt it?
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Re: m15 question 23 [#permalink]
12 Apr 2011, 22:18
gmat1220 wrote: Hello fluke
Is x² - y² divisible by 8?
I think the necessary condition (x+y)or(x-y) or their product divisible by 8 is not sufficient to answer the question. We also need the condition - Is x and y integers? to conclusively answer.
yes to both questions - the answer is yes
yes and no to questions - the answer is no
no and no to questions - the answer is no
I meant we need answers to two questions to answer this question - Is x² - y² divisible by 8? Isnt it? I see. Yes, correct. I somehow thought that you were trying to rephrase the question stem. Gotcha.
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Re: m15 question 23 [#permalink]
20 Feb 2013, 23:14
Why is B not sufficient... x^2-y^2 =(x+y)(x-y) If x+y is divisible by 8 .. so is (x+y)(x-y). Kindly help..
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Re: m15 question 23 [#permalink]
21 Feb 2013, 04:32
Sachin9 wrote: Why is B not sufficient...
x^2-y^2 =(x+y)(x-y)
If x+y is divisible by 8 .. so is (x+y)(x-y).
Kindly help.. Is x^2 - y^2 divisible by 8?(1) x and y are even integers. Clearly insufficient, consider x=y=0 for an YES answer and x=2 and y=0 for a NO answer. (2) x + y is divisible by 8 --> x^2 - y^2=(x+y)(x-y), if one of the multiples is divisible by 8 then so is the product: true for integers, but we are not told that x and y are integers. If x=4.8 and y=3.2, x+y is divisible by 8, BUT x^2 - y^2 is not. Not sufficient. (1)+(2) x and y integers. x+y divisible by 8. Hence (x+y)(x-y) is divisible by 8. Sufficient. Answer: C.
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Re: m15 question 23 [#permalink]
21 Feb 2013, 05:16
Bunuel wrote: Sachin9 wrote: Why is B not sufficient...
x^2-y^2 =(x+y)(x-y)
If x+y is divisible by 8 .. so is (x+y)(x-y).
Kindly help.. Is x^2 - y^2 divisible by 8?(1) x and y are even integers. Clearly insufficient, consider x=y=0 for an YES answer and x=2 and y=0 for a NO answer. (2) x + y is divisible by 8 --> x^2 - y^2=(x+y)(x-y), if one of the multiples is divisible by 8 then so is the product: true for integers, but we are not told that x and y are integers. If x=4.8 and y=3.2, x+y is divisible by 8, BUT x^2 - y^2 is not. Not sufficient. (1)+(2) x and y integers. x+y divisible by 8. Hence (x+y)(x-y) is divisible by 8. Sufficient. Answer: C. x^2-y^2 is ultimately (x+y)(x-y) .. So irrespective of whether x and y are integers or not.. if (x+y) is divisible by 8 , why can't (x+y)* ( x-y) be divisible by 8? What am I missing?
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Re: m15 question 23 [#permalink]
21 Feb 2013, 05:20
Sachin9 wrote: Bunuel wrote: Sachin9 wrote: Why is B not sufficient...
x^2-y^2 =(x+y)(x-y)
If x+y is divisible by 8 .. so is (x+y)(x-y).
Kindly help.. Is x^2 - y^2 divisible by 8?(1) x and y are even integers. Clearly insufficient, consider x=y=0 for an YES answer and x=2 and y=0 for a NO answer. (2) x + y is divisible by 8 --> x^2 - y^2=(x+y)(x-y), if one of the multiples is divisible by 8 then so is the product: true for integers, but we are not told that x and y are integers. If x=4.8 and y=3.2, x+y is divisible by 8, BUT x^2 - y^2 is not. Not sufficient. (1)+(2) x and y integers. x+y divisible by 8. Hence (x+y)(x-y) is divisible by 8. Sufficient. Answer: C. x^2-y^2 is ultimately (x+y)(x-y) .. So irrespective of whether x and y are integers or not.. if (x+y) is divisible by 8 , why can't (x+y)* ( x-y) be divisible by 8? What am I missing? In my post above there is an example for which x^2 - y^2 is NOT divisible by 8 (x=4.8 and y=3.2) because it's not an integer at all.
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Re: m15 question 23 [#permalink]
21 Feb 2013, 08:44
Bunuel wrote:
In my post above there is an example for which x^2 - y^2 is NOT divisible by 8 (x=4.8 and y=3.2) because it's not an integer at all.
So do you mean to say that x^2 - y^2 = (x+y)*(x-y) only when x and y are integers?
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Re: m15 question 23 [#permalink]
22 Feb 2013, 02:15
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Re: m15 question 23 [#permalink]
22 Feb 2013, 02:17
Bunuel wrote: Sachin9 wrote: Bunuel wrote:
In my post above there is an example for which x^2 - y^2 is NOT divisible by 8 (x=4.8 and y=3.2) because it's not an integer at all.
So do you mean to say that x^2 - y^2 = (x+y)*(x-y), only when x and y are integers? No, I didn't say that! Consider this: if x=4.8 and y=3.2, then x^2-y^2=12.8. Is 12.8 divisible by 8? I am getting you.. So , x^2 - y^2 will be divisible by 8 only if x and y are integers..
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Re: m15 question 23 [#permalink]
22 Feb 2013, 02:27
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Re: m15 question 23 [#permalink]
22 Feb 2013, 02:36
Bunuel wrote: No. x^2 - y^2 can be divisible by 8 even if x and y are not integers. For example, x=7.5 and y=0.5. ok. so no such rule for divisibility as such.. we gotto plug in numbers and check .. numbers to be plugged in would depend on the scope of the variables..
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Re: m15 question 23 [#permalink]
22 Feb 2013, 03:09
Is x² - y² divisible by 8? 1. x and y are even integers 2. x + y is divisible by 8 It is a Yes No Data Sufficiency question wherein you should try to disprove the statements rather than prove them. To disprove a statement there should be at least two values which will satisfy and not satisfy the condition in the question or simply you need a yes and a no from the statement. Lets see: Statement (1): Lets substitute for x and y Let us say x = 4 and y = 2 (Satisfies the statement) Putting it in x² - y² we get, 12 which is not divisible by 8, hence we get a 'NO'. Now lets try for a yes, let us say x = 16 and y = 8(Satisfies the statement) x² - y² = 192, which is divisible by 8, so we have a 'YES' Since we have a yes and a no so this statement is not sufficient. Statement (2): Let us do the same for statement 2 X = 6 and Y = 2 (Satisfies the statement) x² - y² = 32, so we get a YES X = 7.6 and Y = 0.4 x² - y² = 57.6, hence it is not divisible by 8 If we combine both we get the answer as it tells us that x and y are integers.
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Re: m15 question 23
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