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Re: Good set of DS 3 [#permalink]
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16 Sep 2010, 11:30
Thanx Bunuel!Some good questions



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Re: Good set of DS 3 [#permalink]
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19 Dec 2010, 17:08
yangsta8 wrote: Bunuel wrote: 4. Is y – x positive? (1) y > 0 (2) x = 1 – y
Statement 1) y>0 Not suff, X could be anything larger or smaller than X. Statement 2) x=1y x+y=1 Let x=3 and y=2 then yx < 0. But if x=1/4 and y=3/4 then yx >0 Not suff. 1 and 2 together) From the example above we have: if x=1/4 and y=3/4 then yx >0 but if we flip it around: if x=3/4 and y=1/4 then yx <0 not suff. ANS = E I selected that both stmts were sufficient together because the examples I chose worked both ways so if x=2 y=3 you get 3(2)=5 or if y=2 than x = (1) so 2(1)=3. Can the insufficiency only be seen with fractional numbers? Thanks.



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Re: Good set of DS 3 [#permalink]
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19 Dec 2010, 17:33
gettinit wrote: yangsta8 wrote: Bunuel wrote: 4. Is y – x positive? (1) y > 0 (2) x = 1 – y
Statement 1) y>0 Not suff, X could be anything larger or smaller than X. Statement 2) x=1y x+y=1 Let x=3 and y=2 then yx < 0. But if x=1/4 and y=3/4 then yx >0 Not suff. 1 and 2 together) From the example above we have: if x=1/4 and y=3/4 then yx >0 but if we flip it around: if x=3/4 and y=1/4 then yx <0 not suff. ANS = E I selected that both stmts were sufficient together because the examples I chose worked both ways so if x=2 y=3 you get 3(2)=5 or if y=2 than x = (1) so 2(1)=3. Can the insufficiency only be seen with fractional numbers? Thanks. Yes, in order to get NO answer you should choose values of x and y from (0, 1), note that this range can give you the YES answer as well. Is \(yx>0\)? > is \(y>x\)?(1) y > 0, not sufficient as no info about \(x\). (2) x = 1  y > \(x+y=1\) > the sum of 2 numbers equal to 1 > we can not say which one is greater. Not sufficient. (1)+(2) \(x+y=1\) and \(y>0\), still can not determine which one is greater: if \(y=0.1>0\) and \(x=0.9\) then \(y<x\) but if \(y=0.9>0\) and \(x=0.1\) then \(y>x\). Not sufficient. Answer: E.
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Re: Good set of DS 3 [#permalink]
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23 Dec 2010, 19:07
thanks Bunuel should have simplified stmt 2 better to understand the fractional solutions. Thank you sir.



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Re: Good set of DS 3 [#permalink]
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31 Jan 2011, 06:33
Hi Bunuel For question # 8, please explain how this is true : either 4y=32 y=8 x=3, xy=24 OR 4y=32 Regards, Subhash
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Re: Good set of DS 3 [#permalink]
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31 Jan 2011, 06:48
subhashghosh wrote: Hi Bunuel
For question # 8, please explain how this is true :
either 4y=32 y=8 x=3, xy=24 OR 4y=32
Regards, Subhash If x and y are nonzero integers and x + y = 32, what is xy? (1) \(4x12y=0\) > \(x=3y\) > \(x\) and \(y\) have opposite signs. So either: \(x=x\) and \(y=y\) > in this case \(x+y=xy=3yy=4y=32\): \(y=8\), \(x=24\), \(xy=24*8\); OR: \(x=x\) and \(y=y\) > \(x+y=x+y=3y+y=4y=32\) > \(y=8\) and \(x=24\) > \(xy=24*8\), the same answer. Sufficient. (2) \(x  y = 16\). Sum this one with th equations given in the stem > \(2x=48\) > \(x=24\), \(y=8\). \(xy=24*8\) (x and y have opposite sign) or \(xy=24*8\) (x and y have the same sign). Multiple choices. Not sufficient. Answer: A.
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Re: Good set of DS 3 [#permalink]
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31 Jan 2011, 19:10
Thanks a lot, I can understand it fully now.
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Re: Good set of DS 3 [#permalink]
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23 Feb 2011, 01:13
For question number 3, consider this:
1st number = 10w+x and 2nd number = 10c+x so three digit number = 100*(wc)+10*(w+c)+x^2
In 1, We are given, wc=x*(w+c)=x^2
or x*(w+cx) = 0 implying either x=0 or w+cx = 0 Since it is given that x is nonzero, we have w+cx = 0 so 1 is sufficient w+c and x being odd just says that w+cx is even number, so insufficient Answer A



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Re: Good set of DS 3 [#permalink]
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07 Aug 2011, 11:53
Quote: If a and b are integers, and a not= b, is ab > 0? (1) a^b > 0 (2) a^b is a nonzero integer.
is true when and does not equal to zero.
(1) > does not equal to zero, but we don't know about , it can be any value, positive or negative. Not sufficient.
(2) is a nonzero integer > can be 1 and any integer, positive or negative. Not sufficient.
(1)+(2) If a=1 and b=2, then ab > 0, but if a=1 and b=2, then ab <0. Not sufficient.
Answer: E. Thanks for the explanation, Bunuel..
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Re: The sum of n consecutive positive integers is 45 [#permalink]
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20 Apr 2012, 21:10
Bunuel wrote: Please find below new set of DS problems:
TIP: many of these problems act in GMAT zone, so beware of ZIP trap.
1. The sum of n consecutive positive integers is 45. What is the value of n? (1) n is even (2) n < 9
Bunuel, Is this approach correct? sum of n consecutive +ve integers = \(\frac{n(n+1)}{2}\) so, \(\frac{n(n+1)}{2}\) = 45 n(n+1) = 90 \(n^{2}+ n  90 = 0\) solving this equation gives n= 10 or 9 Both A and B doesn't help. Hence E.
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Re: The sum of n consecutive positive integers is 45 [#permalink]
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20 Apr 2012, 21:16
ENAFEX wrote: Bunuel wrote: Please find below new set of DS problems:
TIP: many of these problems act in GMAT zone, so beware of ZIP trap.
1. The sum of n consecutive positive integers is 45. What is the value of n? (1) n is even (2) n < 9
Bunuel, Is this approach correct? sum of n consecutive +ve integers = \(\frac{n(n+1)}{2}\) so, \(\frac{n(n+1)}{2}\) = 45 n(n+1) = 90 \(n^{2}+ n  90 = 0\) solving this equation gives n= 10 or 9 Both A and B doesn't help. Hence E. Bunuel, Ignore my request. I found out the mistake. The question does not say sum of first consecutive integers, so, I cant use this formula.
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Re: Good set of DS 3 [#permalink]
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02 May 2012, 08:11
Hi Bunuel/Karishma, Request you to clarify the below colored part. What difference does this makes in the question? Thanks H Bunuel wrote: ANSWERS:
7. If b, c, and d are constants and x^2 + bx + c = (x + d)^2 for all values of x, what is the value of c? (1) d = 3 (2) b = 6
Note this part: "for all values of x" So, it must be true for x=0 > c=d^2 > b=2d (1) d = 3 > c=9 Sufficient (2) b = 6 > b=2d, d=3 > c=9 Sufficient
Answer: D. .
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Re: The sum of n consecutive positive integers is 45 [#permalink]
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29 Jul 2012, 04:31
1. The sum of n consecutive positive integers is 45. What is the value of n? (1) n is even (2) n < 9 Cant we use the formula for sum of n consecutive +ve integers (n)*(n+1)/2 = 45 n^2 +n 90 = 0 n=9 or 10
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Re: The sum of n consecutive positive integers is 45 [#permalink]
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29 Jul 2012, 05:02
dvinoth86 wrote: 1. The sum of n consecutive positive integers is 45. What is the value of n? (1) n is even (2) n < 9
Cant we use the formula for sum of n consecutive +ve integers (n)*(n+1)/2 = 45.
[/color] n^2 +n 90 = 0 n=9 or 10 Cant we use the formula for sum of n consecutive +ve integers (n)*(n+1)/2 = 45. This formula gives the sum of the first n consecutive positive integers: 1,2 3, ..., n.Nowhere is stated that our sequence starts with 1.
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Re: The sum of n consecutive positive integers is 45 [#permalink]
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29 Jul 2012, 05:10
dvinoth86 wrote: 1. The sum of n consecutive positive integers is 45. What is the value of n? (1) n is even (2) n < 9
Cant we use the formula for sum of n consecutive +ve integers (n)*(n+1)/2 = 45 n^2 +n 90 = 0 n=9 or 10 As stated in the previous post \(\frac{n(n+1)}{2}\) gives the sum of first \(n\) positive integers: \(1+2+3+...+n=\frac{n(n+1)}{2}\) and we cannot use that formula since we are not told that we have this case. Check this for more: mathnumbertheory88376.html (Evenly spaced set chapter). Solution of this problem is as follows: The sum of n consecutive positive integers is 45. What is the value of n?(1) n is even > n can be 2: 22+23=45. But it also can be 6 > x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=45 > x=5. At least two values of n are possible. Not sufficient. (2) n<9 > the above example is also valid for this statement, hence not sufficient. (1)+(2) Still at least two values of n are possible. Not sufficient. Answer: E. Hope it's clear.
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Re: The sum of n consecutive positive integers is 45 [#permalink]
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29 Jul 2012, 05:32
Q1 The sum of n consecutive integers is either a multiple of the middle term, in case n is odd, or a multiple of the sum of the two middle terms, in case n is even. (1) Since n is even and 45 is odd, we must have an odd number of pairs in our sequence, such that the sum of each pair is a factor of 45, and it is the same as the sum of the two middle terms. For example, we can have just one pair (22, 23)  or three pairs, each sum being 45/3 = 15  5, 6, 7, 8, 9, 10, with 5+10=6+9=7+8=15. So, (1) is not sufficient. (2) From what we have seen above, (2) is not sufficient either. Just as an example, if n is odd and less than 9, we can have the sequence 14, 15, 16. (1) and (2) taken together is obviously not sufficient. Answer E
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Re: The sum of n consecutive positive integers is 45 [#permalink]
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29 Jul 2012, 05:38
Q7 Since the given equality must hold for any value of x, if we substitute x = 0, we obtain \(c=d^2\). Then, we can immediately see that (1) alone is sufficient, but (2) is not. Answer A
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Re: The sum of n consecutive positive integers is 45 [#permalink]
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29 Jul 2012, 05:49
Q2. Is a product of three integers XYZ a prime? (1) X=Y (2) Z=1 (1) We can take X=1, then Y=1, and taking Z any nonnegative integer will get a nonprime, as the product will be either negative or 0. But if we take X=1, Y=1 and for example Z=2, than XYZ=2, which is a prime. Therefore, (1) is not sufficient. (2) If Z=1, we can take Y=1 as well, and then either X is a prime or not, so the final product XYZ=X, can be or not a prime. Not sufficient. (1) and (2) together: If Z=1 and X=Y, then \(XYZ=X^2\), which can be either 0 (when X=0) or a negative integer. In either case, we won't get a prime number (by definition, a prime must be a positive integer). So, the answer is a definite NO, therefore sufficient. Answer C
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Re: The sum of n consecutive positive integers is 45 [#permalink]
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29 Jul 2012, 06:18
Q3. Multiplication of the two digit numbers wx and cx, where w,x and c are unique nonzero digits, the product is a three digit number. What is w+cx? (1) The three digits of the product are all the same and different from w c and x. (2) x and w+c are odd numbers. (1) If the product is a three digit number, all digits identical, then the number must be of the form AAA=A*111=A*3*37, where A is a nonzero digit. It means that x = 7, and 3A must be a two digit number, which also ends in 7. It follows that 3A = 27, so the numbers are 37 and 27, 37 * 27 = 999, and w+cx=52, sufficient (it doesn't matter who is w and who is c). (2) Since w+c is odd, one of them must be even and the other one odd. Fro example, we can take w=2, c=1, x=3 or w=3, c=2, x=1. 23*13=299, 31*21=651, are both three digit numbers, and w+cx is 0 and 4, respectively. Not sufficient. Answer A. Remark: In the body of the question, w,x and c are unique nonzero digits, shouldn't be "distinct nonzero digits"?
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Re: The sum of n consecutive positive integers is 45 [#permalink]
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29 Jul 2012, 06:27
Q4. Is y – x positive? (1) y > 0 (2) x = 1 – y The question we are asked is in fact is y>x? (1) Not sufficient, as we don't know anything about x. (2) We have x+y=1, again not sufficient. We can have x=y=0.5, or x=0.25 < y=0.75, or x=0.75 > y=0.25 (1) and (2) not sufficient, we can use the examples from the analysis for (2) above. Answer E
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