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General number properties

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by GmatTakerNo.1 » Sun Apr 25, 2010 9:37 am
Hey,
I have here some exercises. Sorry for posting them in one thread, but else I will lose the overview.
Can you guys help me figure these out with´two minute approaches?

1. How many positive three-digit integers have an odd digit in both the tens and units place?
a) 25
b) 225
c) 250
d) 450
e) 500

Answer: B
Here I always got 250 which is C.


2. How many 3-digit integers between 100 and 200 have a digit that is the average (arithmetic mean) of the other 2 digits?
a) 1
b) 7
c) 10
d) 11
e) 19

Answer: D


3. What is the value of 1/2 - 1/3 + 1/4 - 1/5 - 1/6 + 1/7
a) 27/140
b) 37/97
c) 49/101
d) 23/41
e) 41/37

Answer: A

4. Which of the following fractions has a decimal equivalent that is a terminating decimal?
a) 10/189
b) 15/196
c) 16/225
d) 25/144
e) 39/128

Answer E

I really would appreciate if you help me out here.
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by thephoenix » Sun Apr 25, 2010 9:48 am
#1)
we have 5 odd digiys:-1,3,5,7,9
we can make three digits number with the given condition in 9*5*5 ways=225 numbers [for unit digit 5 ways ; for tens digit 5 ways and 9 ways for 100th place]
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by tpr-becky » Sun Apr 25, 2010 11:26 am
The first question is a permutation question

There are 9 digits available for the 100's digit, 5 odd digits available for the 10's and 1's digits so the answer is 9*5*5=225.

The second idea is that two of the numbers have to be even or two of the numbers have to be odd with 2 as the average. if this isn't the case, you won't get an integer for the average. the number also has to start with a 2 because it is between 200 and 300

So

2-0 - the average is 1 - there are 2 versions (210, 201)
2--2 the average is 2 - but only 1 version
2-4 - with average 3 - 2 version
2-6 with average 4 - 2 versions
2-8 with average 5 - 2 versions
2 is the average of 1&3 - 2 versions
for a total of 11
Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA
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by moliver » Sun Apr 25, 2010 12:53 pm
tpr-becky wrote:The first question is a permutation question

There are 9 digits available for the 100's digit, 5 odd digits available for the 10's and 1's digits so the answer is 9*5*5=225.

The second idea is that two of the numbers have to be even or two of the numbers have to be odd with 2 as the average. if this isn't the case, you won't get an integer for the average. the number also has to start with a 2 because it is between 200 and 300

So

2-0 - the average is 1 - there are 2 versions (210, 201)
2--2 the average is 2 - but only 1 version
2-4 - with average 3 - 2 version
2-6 with average 4 - 2 versions
2-8 with average 5 - 2 versions
2 is the average of 1&3 - 2 versions
for a total of 11
I think that tpr-becky wanted to say that the number must be between 100 and 200

For the last question (#4) I think that what you mean by saying terminating decimal is that there are a finit number of decimal in the number, didn't you?
In this case the last option is divided by 128 = 2^6
If the number is divided by 5 or 2 it has a finite numbers of decimals.
the answer c) has not a finite decimal because you have there a 225 = 9*5*5

Question #3 is interesting. Different ideas here. What was your approach?
The hard part do all the maths
Group by the numbers who are positive and who are negative.
or something like this for example
if you do 1/2 - 1/3 = 1/6 so now you can simplify with the -1/6
and now I think that the maths are more straight forward

please let me know if this was helpful
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by GmatTakerNo.1 » Sun Apr 25, 2010 1:18 pm
Thanks for replying.

For question 4 I have the same approach, moliver, but I thought there is maybe a trick.

For question 3 I meant a finite number of decimals by the term "terminating decimal".

Your answers help me a lot, thanks again ;)
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by Ashish8 » Sun Apr 25, 2010 5:09 pm
So exactly what is the strategy for Q4?

Thanks
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by DeepthiRajan » Sun Apr 25, 2010 11:51 pm
If a fraction has to be a terminating decimal, it should have either powers of 2 or 5 in the denominator (eg 2^3 or 5^2)

in case of E, 128 in the denominator can be expressed as 2^7

HTH
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by lcd318 » Mon Apr 26, 2010 8:49 am
For number 3, I ballparked it and got the right answer.

"What is the value of 1/2 - 1/3 + 1/4 - 1/5 - 1/6 + 1/7 ?"

= 0.5 - 0.33 + .25 - .20 - .16 + .14

I got roughly .20, or 1/5. Answer A most closely matches that -- the others aren't even close.
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