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# Several difficult PS and DS questions!!!

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Intern
Joined: 21 Jan 2007
Posts: 23

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Several difficult PS and DS questions!!! [#permalink]

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15 Feb 2007, 11:24
1
KUDOS
Hi to all!!! I have problems in understanding the answers to these questions (which i put in bold)
Thanks alot
Riccardo

SET 6:

Q3:
If a committee of 3 people is to be selected from among 5 married couples so that the
committee does not include two people who are married to each other, how many such
committees are possible?
A. 20

B. 40
C. 50
D. 80
E. 120
------------------------------------------------------------------------------------------------------------
Q4:
√[2√63 + 2/(8+3√7)] =
A. 8 + 3v7
B. 4 + 3v7
C. 8
D. 4
E. v7

Q6:
The ratio of the number of red cars in a certain parking lot to the number of black cars is
3 to 8. If there are 72 black cars in the lot, how many red cars are there in the lot?
A. 11
B. 15
C. 24
D. 27
E. 32
Wy not D??
------------------------------------------------------------------------------------------------------------
Q7:
What is the value of Â¦x + 7Â¦?
(1) Â¦x + 3Â¦= 14
(2) (x + 2)2 = 169

Answer is D, I thought C

SET 6:

Q2:
√[(2*√63) + (2/(8+3*√7))]
=
A. 8 + 3√7
B. 4 + 3√√7
C. 8
D. 4
E. √7

How do u solve it??
------------------------------------------------------------------------------------------------------------
Q3:
For all positive integers m and v, the expression m ** v represents the remainder when m
is divided by v. What is the value [(98**33)**17] â€“ [98**(33**17)]
A. -10
B. -2
C. 8
D. 13
E. 17

Q5:
If k, m, and t are positive integers and
k/6 + m/4 = t/12, do t and 12 have a common factor greater than 1 ?
(1) k is a multiple of 3.
(2) m is a multiple of 3.

Q7:
On an aerial photograph, the surface of a pond appears as circular region of radius
167
inch. If a distance of 1 inch on the photograph corresponds to an actual distance of 2
miles, which of the following is the closest estimate of the actual surface area of the
pond, in square miles?
A. 1.3
B. 2.4
C. 3.0
D. 3.8
E. 5.0

Q10:
If x2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?
(1) a = 1
(2) b = 2

Q11:
If 3^(6x) = 8,100, what is the value of [3^(x â€“ 1)]^3?

A. 90
B. 30
C. 10
D. 310
E. 910

I had really big problems with this one, and I have big problems in general when it comes to big numbers and exponentialsâ€¦ what should I do when I see a big number as a result and the x as the exponent, how do u solve it???

Q14:
Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and
then put back into the bowl; then a second card is drawn. If the cards are drawn at
random and if the sum of the numbers on the cards is 8, what is the probability that one of
the two cards drawn is numbered 5 ?
A. 61
B. 51
C. 31
D. 52
E. 32

If a and b are positive integers such that a â€“ b and
a/b are both even integers, which of the
following must be an odd integer?
A.
a/2
B.
b/2
C.
(A+b)/2
D.
(a+2)/2

E.
(b+2)/2

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15 Feb 2007, 15:51
If a committee of 3 people is to be selected from among 5 married couples so that the
committee does not include two people who are married to each other, how many such
committees are possible?
A. 20
B. 40
C. 50
D. 80
E. 120

Total number of ways to select 3 out of 10=10C3=120
Combination with each couples 8C1 = 8
Total 5 couples 8*5=40

Combi with no couples = 120-40=80

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Posts: 35

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Re: Several difficult PS and DS questions!!! [#permalink]

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15 Feb 2007, 16:47
eribold wrote:

Q4:
√[2√63 + 2/(8+3√7)] =
A. 8 + 3v7
B. 4 + 3v7
C. 8
D. 4
E. v7

√63 = √(9*7) = 3√7

then you have to use (a+b)*(a-b) = aÂ²-bÂ²

Lets begin with solving 2/(8+3√7)
2/(8+3√7) = 2/(8+3√7) * 1
= 2/(8+3√7) * (8-3√7)/(8-3√7)
= 2*(8-3√7) / (8+3√7)* (8-3√7)

So you have

(8+3√7)*(8-3√7) = 8Â² -(3√7)Â² = 64-63 = 1

an then

2/(8+3√7) = 2*(8-3√7)

Now the whole thing

√[2√63 + 2/(8+3√7)] = √[2*3√7 + 2*(8-3√7)]
=√[2*3√7 + 16 -2*3√7] =√16 = 4
Attachments

Clipboard01_jvujuc.jpg [ 13.34 KiB | Viewed 4704 times ]

Last edited by jvujuc on 16 Feb 2007, 01:20, edited 2 times in total.

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Re: Several difficult PS and DS questions!!! [#permalink]

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15 Feb 2007, 17:03
eribold wrote:

Q3:
For all positive integers m and v, the expression m ** v represents the remainder when m
is divided by v. What is the value [(98**33)**17] â€“ [98**(33**17)]
A. -10
B. -2
C. 8
D. 13
E. 17

This is my logic how to calculate it quickly

if by definition of '**' 99**33=0, then is 98**33 = 32
34**17=0 then is 32**17=15
(98**33)**17 = 15

33**17=16

16*6 = 96; so 96**16=0 and 98**16 = 2

15-2 = 13

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Re: Several difficult PS and DS questions!!! [#permalink]

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15 Feb 2007, 17:37
eribold wrote:
Q11:
If 3^(6x) = 8,100, what is the value of [3^(x â€“ 1)]^3?

A. 90
B. 30
C. 10
D. 310
E. 910

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15 Feb 2007, 19:08
1
KUDOS
Q10:
If x2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?
(1) a = 1
(2) b = 2

x2 + 3x + c = x2 + xb + xa + ab
= x2 + x(a+b) + ab
cancel out x2 from both side,

3x + c = x(a+b) + ab

suppose we know that a = 1:

3x + c = x(1+b) + b
= x + xb + b

since you have to have x to make 3x,

3x = x + xb
2x = xb
b=2

c = b = 2.

Similarly, b = 2 is sufficient to determine c.

Hope this explains...

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Re: Several difficult PS and DS questions!!! [#permalink]

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15 Feb 2007, 23:37
[quote="eribold"]

Q7:
What is the value of Â¦x + 7Â¦?
(1) Â¦x + 3Â¦= 14
(2) (x + 2)2 = 169

(1) Â¦x + 3Â¦= 14
-(x+3)=14
x=11 and
(x+3)=14
x=11 suff

(2) (x + 2)2 = 169 I guess this should be (x+2)^2=169
(x+2)=13
x=11

Answer is D, I thought C

SET 6:

Q2:
√[(2*√63) + (2/(8+3*√7))]
=
A. 8 + 3√7
B. 4 + 3√√7
C. 8
D. 4
E. √7

√[(2*√63) + (2/(8+3*√7))]=
√[(2*√63) + (2/(8+√63))] I got (2/(8+√63) from (2/(8+3*√7) since 3*√7 is the same as √63

√[(2*√63) + (2/(8+√63))]=
√[{(2*√63)*(8+√63) + 2}/(8+√63))]=
√[{(16*√63+128}/(8+√63))]=
√[{16*(√63+8)}/(8+√63))]=
√[16]=4

------------------------------------------------------------------------------------------------------------
Q3:
For all positive integers m and v, the expression m ** v represents the remainder when m
is divided by v. What is the value [(98**33)**17] – [98**(33**17)]
A. -10
B. -2
C. 8
D. 13
E. 17
[(98**33)**17] – [98**(33**17)]=
(98**33)=32
(32**17)=15
(33**17)=16
(98**16)=2
15-2 =13

Q11:
If 3^(6x) = 8,100, what is the value of [3^(x – 1)]^3?

A. 90
B. 30
C. 10
D. 310 must be 10/3
E. 910 must be 10/9
_________________

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Re: Several difficult PS and DS questions!!! [#permalink]

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16 Feb 2007, 02:01
eribold wrote:
Q7:
On an aerial photograph, the surface of a pond appears as circular region of radius
167
inch. If a distance of 1 inch on the photograph corresponds to an actual distance of 2
miles, which of the following is the closest estimate of the actual surface area of the
pond, in square miles?
A. 1.3
B. 2.4
C. 3.0
D. 3.8
E. 5.0

Am I missing something here, or is the text wrong again?

If a distance of 1 inch on the photograph corresponds to an actual distance of 2 miles, then is the actual radius of a pond 167 * 2 miles

Surface of the circle is radius^2*PI
Attachments

Clipboard02_jvujuc.jpg [ 1.87 KiB | Viewed 4696 times ]

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Re: Several difficult PS and DS questions!!! [#permalink]

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16 Feb 2007, 02:41
eribold wrote:
If a and b are positive integers such that a â€“ b and
a/b are both even integers, which of the
following must be an odd integer?
A.
a/2
B.
b/2
C.
(A+b)/2
D.
(a+2)/2

E.
(b+2)/2

E (even number)
O (odd number)

Substraction table

Quote:
6-2 = 4; 10-4=6 => E-E=E
8-3=5; 10-1=9 => E-O=O
9-2=7; 11-2=9 => O-E=O
9-3=6; 3-1=2 => O-O=E

If a-b is even, then both a and b must be either even or odd

Multiplication table:

Quote:
2*2 = 4; 4*4=16 => E*E=E
2*3=6; 4*5=20 => E*O=E
3*3=9; 5*5=25 => O*O=O

Division table:

Quote:
E/E=E
E/E=O
E/O=E
O/O=O

Our second require tells us that a/b is even, then either a must be even and b odd, or both a and b must be even

Require 1 AND require 2, give us that both a and b must be even, which doesn't match to any given solution uniquely

What's wrong here?

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Re: Several difficult PS and DS questions!!! [#permalink]

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18 Feb 2007, 22:07
jainvineet wrote:
Yurik79 wrote:
eribold wrote:

Q7:
What is the value of Â¦x + 7Â¦?
(1) Â¦x + 3Â¦= 14
(2) (x + 2)2 = 169

[b](1) Â¦x + 3Â¦= 14
-(x+3)=14
x=11 and ------> should,nt this be x = -17(x+3)=14
x=11 suff

Please see the stmt in red.

You re right my fault))
Hmm it is C
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08 Mar 2007, 04:50
Q7: What is the value of Â¦x + 7Â¦?
(1) Â¦x + 3Â¦= 14
(2) (x + 2)^2 = 169

(1) |x+3| = 14
Here x is either 11 or -17.

if x = 11
|11+3| = 14

and if x = -17
|-17+3 = -14| = 14

Since we have two values for x, the statement is NOT-SUFFICIENT. (In DS we must have ONE confirmed answer)

(2) (x+2)^2 = 169
(x+2) = 13
x = 11

Statement (2) has only one confirmed answer for x, so B alone is SUFFICIENT.

Am I right?

Another case suppose statement (2) is (x+2)2 = 169 as given by original poster.
(x+2) = 169/2 = 84.5
x = 82.5

|x+7| will be |84.5 + 7| or |91.5| (First time for me to see a fraction/decimal in absolute value).......any help here?

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08 Mar 2007, 04:56
Damager wrote:
If a committee of 3 people is to be selected from among 5 married couples so that the
committee does not include two people who are married to each other, how many such
committees are possible?
A. 20
B. 40
C. 50
D. 80
E. 120

Total number of ways to select 3 out of 10=10C3=120
Combination with each couples 8C1 = 8
Total 5 couples 8*5=40

Combi with no couples = 120-40=80

Sorry, the part written in red is not clear. Please explain it. Thanks.

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08 Mar 2007, 05:19
ricokevin wrote:
Q10:
If x2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?
(1) a = 1
(2) b = 2

x2 + 3x + c = x2 + xb + xa + ab
= x2 + x(a+b) + ab
cancel out x2 from both side,

3x + c = x(a+b) + ab

suppose we know that a = 1:

3x + c = x(1+b) + b
= x + xb + b

since you have to have x to make 3x,

3x = x + xb (where are c and b?)
2x = xb
b=2

c = b = 2.

Similarly, b = 2 is sufficient to determine c.

Hope this explains...

You are taking a = 1. Aren't you clearly making statement C as SUFFICIENT by taking a = 1 here because it is given in (1).

Please explain the parts given in red. I am confused.

Thanks.

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08 Mar 2007, 09:23
Q5:
If k, m, and t are positive integers and
k/6 + m/4 = t/12, do t and 12 have a common factor greater than 1 ?
(1) k is a multiple of 3.
(2) m is a multiple of 3.

Solution:
=>(2k+3m)/12 = t/12
=>t=2k+3m

If k is a multiple of 3, then t=2*3 + 3m, Values of t are 2*3 +3*0 = 6, 2*3 + 3*1= 9 and so on. Every value of t has a factor which is common to a factor of 12 and greater than 1, i.e., 3.
If m is a multiple of 3, then t=2k + 3*3. Values of t are 2*0 + 3*3=9, 2*1 +3*3=11 and so on. Considering the value of t we can confirm that 11 and 12 do not have common factor.

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08 Mar 2007, 09:33
Q7:
On an aerial photograph, the surface of a pond appears as circular region of radius
167
inch. If a distance of 1 inch on the photograph corresponds to an actual distance of 2
miles, which of the following is the closest estimate of the actual surface area of the
pond, in square miles?
A. 1.3
B. 2.4
C. 3.0
D. 3.8
E. 5.0

Solution:
Area = pi * r^2 = pi * (167*2)^2 = 22 * 111556 /7 = 350605 square miles.
Could you please verify the numbers? Seems something is not right.

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08 Mar 2007, 09:39
Q10:
If x2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?
(1) a = 1
(2) b = 2

Solution:
Right side of the equation is : x^2 + x(a+b) + ab
So, a+b=3 and ab=c
St1) If a =1 then b=2, and ab=c=2. Sufficient
St2) If b=2, then a=1, and ab=c=2. Sufficient

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08 Mar 2007, 22:05
Thanks rdg!

I got it!

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08 Mar 2007, 23:25
rdg wrote:
Q7:
On an aerial photograph, the surface of a pond appears as circular region of radius
167
inch. If a distance of 1 inch on the photograph corresponds to an actual distance of 2
miles, which of the following is the closest estimate of the actual surface area of the
pond, in square miles?
A. 1.3
B. 2.4
C. 3.0
D. 3.8
E. 5.0

Solution:
Area = pi * r^2 = pi * (167*2)^2 = 22 * 111556 /7 = 350605 square miles.
Could you please verify the numbers? Seems something is not right.

True. There is something wrong with the question.

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06 Oct 2009, 20:57
rdg wrote:
Q10:
......
So, a+b=3 and ab=c

Please explain. How do you come to this conclusion?

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Re: Several difficult PS and DS questions!!! [#permalink]

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07 Oct 2009, 11:33
1
This post was
BOOKMARKED
eribold wrote:

SET 6:

Q3:
If a committee of 3 people is to be selected from among 5 married couples so that the
committee does not include two people who are married to each other, how many such
committees are possible?
A. 20

B. 40
C. 50
D. 80
E. 120
------------------------------------------------------------------------------------------------------------

I answered this a different way...

First person in committee can be 10 people.
Second choice can be 8 (10 minus first choice minus first choice wife)
Third choice can be 6(8 minus second minus second wife)

Then, divide by the number of ways to arrange 3 people which is 6.

(10*8*6)/6 and voila! 80.

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Re: Several difficult PS and DS questions!!!   [#permalink] 07 Oct 2009, 11:33

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