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Math Expert V
Joined: 02 Sep 2009
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Re: The Discreet Charm of the DS  [#permalink]

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sourabhsoni wrote:
1. Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y?
(1) x^2+y^2<12
(2) Bonnie and Clyde complete the painting of the car at 10:30am

The catch is that they are working independently.

stmt 1 - no relation there are can be multiple values of x and y
stmt 2 - both started at same time, finished at same time with no breaks means they have same working rate proves x = y
sufficient

The logic for (2) is not correct, (though I'm not saying that (2) is insufficient). Even if two entities have different rates if they work together they both stop when the job is done.
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Math Expert V
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Re: The Discreet Charm of the DS  [#permalink]

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sourabhsoni wrote:
2. Is xy<=1/2?
(1) x^2+y^2=1
(2) x^2-y^2=0

My funda - Area of square is largest among all the quadilateral with same perimeter.
Stmt 1 - Only possible values of x and y are 1/Sqrt(2). So sufficient as xy = 1/2
Stmt 2 - Only says x and y are equal. Not sufficient

You are close to correct reasoning for (1), though from it you can not say that xy=1/2 and the only possible value for x and y are 1/Sqrt(2). Consider the following example: 0^1+1^2=1.

As for (2): x^2-y^2=0 doesn't mean that x=y.
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Re: The Discreet Charm of the DS  [#permalink]

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sourabhsoni wrote:
3. If a, b and c are integers, is abc an even integer?
(1) b is halfway between a and c
(2) a = b - c

Funda for product abc to be even, if any one of them even then product will be even.

Stmt 1 - says b = (a+c)/2
means a+c is some even number.
E + E also results in even
O + O also results in Even and b can be anything even or odd
so not sufficient.

Stmt 2 - says a = b - c
say worst condition b an c are odd . will results in a even. or lets says any one among b or c is even then a off but since one number is even the product will be even so sufficient.

That's correct. +1.
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Re: The Discreet Charm of the DS  [#permalink]

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1)b
2)a
3)b
4)d
5)d
6)e
7)d
8)c
9)e
10)a
11)d
12)a
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Re: The Discreet Charm of the DS  [#permalink]

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Bunuel wrote:
sourabhsoni wrote:
1. Bonnie can paint a stolen car in x hours, and Clyde can paint the same car in y hours. They start working simultaneously and independently at their respective constant rates at 9:45am. If both x and y are odd integers, is x=y?
(1) x^2+y^2<12
(2) Bonnie and Clyde complete the painting of the car at 10:30am

The catch is that they are working independently.

stmt 1 - no relation there are can be multiple values of x and y
stmt 2 - both started at same time, finished at same time with no breaks means they have same working rate proves x = y
sufficient

The logic for (2) is not correct, (though I'm not saying that (2) is insufficient). Even if two entities have different rates if they work together they both stop when the job is done.

-----------------------------

yes but isn't it correct to say that when they are working independently and starting at same time (as per the question) and ending at same time as per stmt 2 then they must be working at same rate - i.e. X = Y...

As stmt 2 doesn't say they are not working together.
Math Expert V
Joined: 02 Sep 2009
Posts: 58954
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sourabhsoni wrote:
yes but isn't it correct to say that when they are working independently and starting at same time (as per the question) and ending at same time as per stmt 2 then they must be working at same rate - i.e. X = Y...

As stmt 2 doesn't say they are not working together.

No, that's not correct. Again when: two or more entities (machines, people, ...) are working together they all stop working when the job is done, no matter what their respective rates are. I think that you are thrown away by the phrase "they start working simultaneously and independently", which simply means that they start at the same time and work together (obviously they will also end the work at the same time, when the work is done).

Hope it's clear.
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Re: The Discreet Charm of the DS  [#permalink]

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kys123 wrote:
1)b
2)a
3)b
4)d
5)d
6)e
7)d
8)c
9)e
10)a
11)d
12)a

8 correct answers out of 12.

Well done.

kys123 wrote:
1) statement 2 means

rate = 1/x + 1/y = 4/3 (1/[45 mins/ 60 mins]).

The only integer that would work is 1 n 3. Therefore x =/=y. Since X has to be 1 or 3 and Y is whatever X isn't.

That's correct, though there is another way of doing this.
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GMAT 1: 760 Q51 V41 Re: The Discreet Charm of the DS  [#permalink]

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7.A
8.C
9.B
10.C
11.D
12.B
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Re: The Discreet Charm of the DS  [#permalink]

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6. If a and b are integers and ab=2, is a=2?
(1) b+3 is not a prime number
(2) a>b

Possible values of a and b are : (1,2), (2,1), (-1,-2), (-2,-1)
we have to find out if a = 2 or get if b is 1.

Stmt 1 - b+3 is prime number. Possible values of b 2 and -1 Not sufficient.

Stmt 2 a > b Pssible values of b are 1, -2. Not sufficient

Combining stmt 1 and stmt 2 no common answers. So insufficient.

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Re: The Discreet Charm of the DS  [#permalink]

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9. If x and y are negative numbers, is x<y?
(1) 3x + 4 < 2y + 3
(2) 2x - 3 < 3y - 4

Given x is -ve and y is -ve

Stmt 1 - 3x + 4 < 2y + 3 which can be written as
3x < 2y - 1
suppose x < y
then 3x < 3y

You cannot dedude from here. So insufficient.

Stmt 2 - 2x - 3 < 3y - 4 which cane be written as
2x + 1 < 3y
which can be furhter written as 2y > 3y

therefore 2x + 1 < 2y even after 1 2x is smaller than 2y that proves x < y.

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Re: The Discreet Charm of the DS  [#permalink]

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10. The function f is defined for all positive integers a and b by the following rule: f(a,b)=(a+b)/GCF(a,b), where GCF(a,b) is the greatest common factor of a and b. If f(10,x)=11, what is the value of x?
(1) x is a square of an integer
(2) The sum of the distinct prime factors of x is a prime number.

Given 10 + x / GCF (10,x) = 11. Possible values of GCF(10,x) = 1,2,5,10.
So 10+x can be 11, 22, 55, 110 ; which will result in x = 1,12, 45, 100

Stmt 1 - x can be 1 and 10 so not sufficient.
Stmt 2 - x can be 12 , 100 so not sufficient.

Combining stmt 1 and stmt 2 we get x = 100.

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Re: The Discreet Charm of the DS  [#permalink]

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11. If x and y are integers, is x a positive integer?
(1) x*|y| is a prime number.
(2) x*|y| is non-negative integer.

prime # are always positive

Stmt 1 - |y| will be always positive to x*|y| to be prime z has to be positve. Sufficient
Stmt 2 - Same concept x will be positive number Sufficient

Math Expert V
Joined: 02 Sep 2009
Posts: 58954
Re: The Discreet Charm of the DS  [#permalink]

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Solutions for: 4, 5, 7, 8, 9, and 10 are correct. +1 for each.

sourabhsoni wrote:
6. If a and b are integers and ab=2, is a=2?
(1) b+3 is not a prime number
(2) a>b

Possible values of a and b are : (1,2), (2,1), (-1,-2), (-2,-1)
we have to find out if a = 2 or get if b is 1.

Stmt 1 - b+3 is prime number. Possible values of b 2 and -1 Not sufficient.

Stmt 2 a > b Pssible values of b are 1, -2. Not sufficient

Combining stmt 1 and stmt 2 no common answers. So insufficient.

As for this one: first of all (1) says that b+3 is NOT a prime number.

Next, on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. So, we can not have the case when (1) says that b is either 2 or -1 and (2) says that b is either 1 or -2, because in this case statements would contradict each other.

Hope it's clear.

P.S. Funny thing: answer is still E.
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Re: The Discreet Charm of the DS  [#permalink]

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Bunuel wrote:
sourabhsoni wrote:
2. Is xy<=1/2?
(1) x^2+y^2=1
(2) x^2-y^2=0

My funda - Area of square is largest among all the quadilateral with same perimeter.
Stmt 1 - Only possible values of x and y are 1/Sqrt(2). So sufficient as xy = 1/2
Stmt 2 - Only says x and y are equal. Not sufficient

You are close to correct reasoning for (1), though from it you can not say that xy=1/2 and the only possible value for x and y are 1/Sqrt(2). Consider the following example: 0^1+1^2=1.

As for (2): x^2-y^2=0 doesn't mean that x=y.

1) x2 + y2 = 1 is a circle with radius 1, and origin as center. We are only concerned with 1st and 3rd quad (think why? ), Draw a line y=x which intersects circle at x=y=1/sqrt(2). We can observe, as x becomes greater than 1/sqrt2, y gets lesser than 1/sqrt2 moving on the circle (below y=x line). Hence xy<= 1/2. Similarly, as y becomes greater than 1/sqrt2, x gets lesser than 1/sqrt2 moving on the circle (above y=x line). Hence xy<= 1/2. Hence sufficient.

For more mathematically inclined, draw graph of xy=1/2. It has only one point of contact with the circle, tangential at x=y=1/sqrt(2). Yes, the answer to the question is indeed A. +1.

Though let me point out that there are at least two other solutions that are shorter and easier. I'll post them in couple of days, after some more discussion.
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Bunuel wrote:
Bunuel wrote:
2. Is xy<=1/2?
(1) x^2+y^2=1
(2) x^2-y^2=0

1) x2 + y2 = 1 is a circle with radius 1, and origin as center. We are only concerned with 1st and 3rd quad (think why? ), Draw a line y=x which intersects circle at x=y=1/sqrt(2). We can observe, as x becomes greater than 1/sqrt2, y gets lesser than 1/sqrt2 moving on the circle (below y=x line). Hence xy<= 1/2. Similarly, as y becomes greater than 1/sqrt2, x gets lesser than 1/sqrt2 moving on the circle (above y=x line). Hence xy<= 1/2. Hence sufficient.

For more mathematically inclined, draw graph of xy=1/2. It has only one point of contact with the circle, tangential at x=y=1/sqrt(2). Yes, the answer to the question is indeed A. +1.

Though let me point out that there are at least two other solutions that are shorter and easier. I'll post them in couple of days, after some more discussion.

IMO, if you can imagine drawing the circle and y=x line, it takes less than 30 sec. to figure it out. It only takes so much longer to explain in text. And ofcourse, no need to draw the xy graph. Will wait though for the even faster method, if any. _________________
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Bunuel wrote:
Bunuel wrote:
If you answered this question in less than 30 sec using this approach then all I can say is great job!

As for the easier/faster solution, little hint: it involves simplest algebraic manipulation.

F***ing good !

(x-y)2 = 1-2xy >=0 => xy>=1/2.

Now this should take 15sec ! That's it. +1 again.

Now tell me which one is easier/faster?

Just a little typo there: xy<=1/2.

Haha. I said, then and there, this should take 15 sec. i.e. double the time I took.

P.S. : As we see, the co-ordinate geometry method might not be the best way to solve this particular problem. Having said that I must say one should keep this approach at the back of the mind. Solving complex inequalities can be monumental at times, and certainly more prone to errors while co-ordinate geometry is graphical, clean and quick.
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Re: The Discreet Charm of the DS  [#permalink]

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Hey Bunuel can I ask a question for 12?

We know 6a=3b

And for statement one:

ac =6b. Can't 6b =12a

Then it becomes ac=12a ==> c=12. I know it's wrong since if a is 0 then they will be equal regardless, but can you explain why what I did was wrong?
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Re: The Discreet Charm of the DS  [#permalink]

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kys123 wrote:
Hey Bunuel can I ask a question for 12?

We know 6a=3b

And for statement one:

ac =6b. Can't 6b =12a

Then it becomes ac=12a ==> c=12. I know it's wrong since if a is 0 then they will be equal regardless, but can you explain why what I did was wrong?

Also,

6a = 3b = 7c

Can we say a/b= 1/2, b/c = 7/3, and a/c = 7/6
a) ac = 6b, therefore c = 6b/a
substituting this in b/c => b / (6b/a) = 7/3 => a =14, b=28, c = 12

Isnt A also sufficient? Am I ignoring something?
Math Expert V
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Re: The Discreet Charm of the DS  [#permalink]

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kys123 wrote:
Hey Bunuel can I ask a question for 12?

We know 6a=3b

And for statement one:

ac =6b. Can't 6b =12a

Then it becomes ac=12a ==> c=12. I know it's wrong since if a is 0 then they will be equal regardless, but can you explain why what I did was wrong?

ac=12a (here you can not reduce by a and write c=12 as you exclude possibility of a=0) --> a(c-12)=0 --> either a=0 OR c=12. So, we get either a=b=c=0 or a=14, b=28 and c=12.

nhemdani wrote:
Also,

6a = 3b = 7c

Can we say a/b= 1/2, b/c = 7/3, and a/c = 7/6
a) ac = 6b, therefore c = 6b/a
substituting this in b/c => b / (6b/a) = 7/3 => a =14, b=28, c = 12

Isnt A also sufficient? Am I ignoring something?

Your doubt is partially addressed above, though there is another thing: from 6a = 3b you can not write a/b=1/2 because b can be zero and we can not divide by zero. The same for other ratios you wrote.

Hope it's clear.
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Re: The Discreet Charm of the DS  [#permalink]

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All,

7. A certain fruit stand sold total of 76 oranges to 19 customers. How many of them bought only one orange?
(1) None of the customers bought more than 4 oranges
(2) The difference between the number of oranges bought by any two customers is even

In respect to the question above, I assumed that any two of those 19 customer might have bought 5 & 3 oranges and hence I, marked the option insufficient. Bunnel have equated and treated the option in totally different way. I ,lack the skill to convert these sort of condition in to equation.

please can some post or point to the list of similar Word translation sentences and how to convert them in to equation. Im very new to GMAT club so please forgie me if this is the repeated posting.

Thanks,
Vids Re: The Discreet Charm of the DS   [#permalink] 25 Feb 2012, 05:27

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