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

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15 Feb 2007, 11:24

1

This post received KUDOS

Hi to all!!! I have problems in understanding the answers to these questions (which i put in bold)
Could you please help me out in explaining them to me??
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
Answer:
------------------------------------------------------------------------------------------------------------
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.
Answer is A

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
Answer is D!!

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

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

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

Show Tags

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

------------------------------------------------------------------------------------------------------------
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
_________________

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

Show Tags

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 ]

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

Show Tags

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

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.

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.
Answer is A

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.

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.

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

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

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.

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

Show Tags

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 Answer: ------------------------------------------------------------------------------------------------------------

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.

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