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# The Discreet Charm of the DS

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Math Expert
Joined: 02 Sep 2009
Posts: 59074
The Discreet Charm of the DS  [#permalink]

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02 Feb 2012, 04:15
59
190
I'm posting the next set of medium/hard DS questions. I'll post OA's with detailed explanations after some discussion. Please, post your solutions along with the answers. Good luck!

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

Solution: the-discreet-charm-of-the-ds-126962-20.html#p1039633

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

Solution: the-discreet-charm-of-the-ds-126962-20.html#p1039634

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

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039637

4. How many numbers of 5 consecutive positive integers is divisible by 4?
(1) The median of these numbers is odd
(2) The average (arithmetic mean) of these numbers is a prime number

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039645

5. What is the value of integer x?
(1) 2x^2+9<9x
(2) |x+10|=2x+8

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039650

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

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039651

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

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039655

8. If x=0.abcd, where a, b, c and d are digits from 0 to 9, inclusive, is x>7/9?
(1) a+b>14
(2) a-c>6

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039662

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

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039665

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.

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039671

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.

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039678

12. If 6a=3b=7c, what is the value of a+b+c?
(1) ac=6b
(2) 5b=8a+4c

Solution: the-discreet-charm-of-the-ds-126962-40.html#p1039680
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Math Expert
Joined: 02 Sep 2009
Posts: 59074
Re: The Discreet Charm of the DS  [#permalink]

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05 Feb 2012, 04:37
10
40
2. Is xy<=1/2?

(1) x^2+y^2=1. Recall that $$(x-y)^2\geq{0}$$ (square of any number is more than or equal to zero) --> $$x^2-2xy+y^2\geq{0}$$ --> since $$x^2+y^2=1$$ then: $$1-2xy\geq{0}$$ --> $$xy\leq{\frac{1}{2}}$$. Sufficient.

(2) x^2-y^2=0 --> $$|x|=|y|$$. Clearly insufficient.

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Posts: 234
Location: India
GMAT 1: 760 Q51 V41
Re: The Discreet Charm of the DS  [#permalink]

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02 Feb 2012, 04:58
2
1.B
2.A
3.B
4.D
5.A
6.E
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Re: The Discreet Charm of the DS  [#permalink]

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02 Feb 2012, 06:55
1. B
2. A
3. B
4. D
5. D
6. E
7. D
8. C
9. B
10. C
11. D
12. E
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Re: The Discreet Charm of the DS  [#permalink]

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02 Feb 2012, 07:48
time to get cracking... thanks for posting
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Joined: 16 Jan 2012
Posts: 6
Re: The Discreet Charm of the DS  [#permalink]

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02 Feb 2012, 11:55
1-b
2-a
3-b
4-a
5-b
6-e
7-d
8-b
9-e
10-a
11-d
12-a
Intern
Joined: 13 Jul 2011
Posts: 11
Re: The Discreet Charm of the DS  [#permalink]

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02 Feb 2012, 19:01
Ans:
1-B
2-A
3-A
4-E
5-D
6-E
7-C
8-A
9-C
10-A
11-D
12-D
Math Expert
Joined: 02 Sep 2009
Posts: 59074
Re: The Discreet Charm of the DS  [#permalink]

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03 Feb 2012, 03:36
1.B
2.A
3.B
4.D
5.A
6.E

5 correct answers out of 6.

sourabhsoni wrote:
1. B
2. A
3. B
4. D
5. D
6. E
7. D
8. C
9. B
10. C
11. D
12. E

10 correct answers out of 12.

1-b
2-a
3-b
4-a
5-b
6-e
7-d
8-b
9-e
10-a
11-d
12-a

7 correct answers out of 12.

vinayaerostar wrote:
Ans:
1-B
2-A
3-A
4-E
5-D
6-E
7-C
8-A
9-C
10-A
11-D
12-D

4 correct answers out of 12.

Good job everyone! By the way it's better if you post the solutions along with the answers: others will benefit with your approaches and you'll get 1 Kudos point per correct solution.

Will post explanations in couple of days, so that to give some more time to those who want to participate.
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Re: The Discreet Charm of the DS  [#permalink]

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03 Feb 2012, 07:51
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

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

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03 Feb 2012, 07:56
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
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Posts: 59074
Re: The Discreet Charm of the DS  [#permalink]

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03 Feb 2012, 07:57
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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Posts: 59074
Re: The Discreet Charm of the DS  [#permalink]

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03 Feb 2012, 08:00
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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03 Feb 2012, 08:01
1
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.

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Joined: 02 Sep 2009
Posts: 59074
Re: The Discreet Charm of the DS  [#permalink]

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03 Feb 2012, 08:04
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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03 Feb 2012, 08:43
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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03 Feb 2012, 08:52
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.
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Posts: 59074
Re: The Discreet Charm of the DS  [#permalink]

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03 Feb 2012, 08:59
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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03 Feb 2012, 09:00
1
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.
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Re: The Discreet Charm of the DS  [#permalink]

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03 Feb 2012, 09:08
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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Re: The Discreet Charm of the DS  [#permalink]

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03 Feb 2012, 14:52
7.A
8.C
9.B
10.C
11.D
12.B
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Re: The Discreet Charm of the DS   [#permalink] 03 Feb 2012, 14:52

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