Problem Solving

(1001^2 - 999^2)/(101^2 - 99^2) =

also

What is the greatest prime factor of 4^17 - 2^28?

also

A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?


Please tell me how to get this. Thanks in advance.

1)
Write
1001 as 1000+1
999 as 1000-1
101 as 100+1
99 as 100-1
and then use a^2-B^2 = a+b * a-b

2)Write 4^17 as 2^34 and then the expression becomes

2^28(2^6-1)

2^18 * 63
=2^18 * 3 * 3 * 7

Hence 7 as it is the largest of 2,3,7.

3)

Either 1Kind of cheese and 1 kind of fruit OR
2 kinds of cheese and 2 kind of Fruit.

i.e : 6c1*2c1 + 6c2*2c2
=12+15=37 kinds of platters

Whats the OA for 3)?

sanjana wrote:1)
Write
1001 as 1000+1
999 as 1000-1
101 as 100+1
99 as 100-1
and then use a^2-B^2 = a+b * a-b

2)Write 4^17 as 2^34 and then the expression becomes

2^28(2^6-1)

2^18 * 63
=2^18 * 3 * 3 * 7

Hence 7 as it is the largest of 2,3,7.

3)

Either 1Kind of cheese and 1 kind of fruit OR
2 kinds of cheese and 2 kind of Fruit.

i.e : 6c1*2c1 + 6c2*2c2
=12+15=37 kinds of platters

Whats the OA for 3)?

OA for 3) is 27. So I guess there is a math error that you are probably making or maybe the software is wrong. Either way I'm not getting your abbreviations or explanations. Can you please break down both 1 and 3 a little more?

What is 6c1*2c1 and 6c2*2c2?

For 1, after doing the a^2 - b^2 I still don't see how you can reduce the fraction to 10. They are completely different numbers. Can you break that down for me a little more. Thanks.

sanjana wrote:1)
Write
1001 as 1000+1
999 as 1000-1
101 as 100+1
99 as 100-1
and then use a^2-B^2 = a+b * a-b

2)Write 4^17 as 2^34 and then the expression becomes

2^28(2^6-1)

2^18 * 63
=2^18 * 3 * 3 * 7

Hence 7 as it is the largest of 2,3,7.

3)

Either 1Kind of cheese and 1 kind of fruit OR
2 kinds of cheese and 2 kind of Fruit.

i.e : 6c1*2c1 + 6c2*2c2
=12+15=37 kinds of platters

Whats the OA for 3)?

OA for 3) is 27. So I guess there is a math error that you are probably making or maybe the software is wrong. Either way I'm not getting your abbreviations or explanations. Can you please break down both 1 and 3 a little more?

What is 6c1*2c1 and 6c2*2c2?

For 1, after doing the a^2 - b^2 I still don't see how you can reduce the fraction to 10. They are completely different numbers. Can you break that down for me a little more. Thanks.

oh well!
15+12 is 27 not 37! GMAT prep is never wrong.

When u use a^2 - b^2 u will get

(1000+1+1000-1)(1000+1-1000+1)
------------------------------
(100+1+100-1)(100+1-100+1)

=2000*2
------
200*2

=10

sanjana wrote:oh well!
15+12 is 27 not 37! GMAT prep is never wrong.

When u use a^2 - b^2 u will get

(1000+1+1000-1)(1000+1-1000+1)
------------------------------
(100+1+100-1)(100+1-100+1)

=2000*2
------
200*2

=10

Sanja, I do appreciate your help. I'm wondering how I can get my mind to start seeing these things....

Can you tell me about number 3. I don't understand the abbreviations of 6c1*2c1. Of equal importance what I'm getting from this is that you are saying 6*2 for this abbreviation. I don't get how you got 15 for the second abbreviation (6c2*2c2). Thanks.

mpaudena wrote:

sanjana wrote:oh well!
15+12 is 27 not 37! GMAT prep is never wrong.

When u use a^2 - b^2 u will get

(1000+1+1000-1)(1000+1-1000+1)
------------------------------
(100+1+100-1)(100+1-100+1)

=2000*2
------
200*2

=10

Sanja, I do appreciate your help. I'm wondering how I can get my mind to start seeing these things....

Can you tell me about number 3. I don't understand the abbreviations of 6c1*2c1. Of equal importance what I'm getting from this is that you are saying 6*2 for this abbreviation. I don't get how you got 15 for the second abbreviation (6c2*2c2). Thanks.

6C1 * 2C1

6C1 = 6!/5!1!
2C1 = 2!/1!

I like using Anagrams to help visualize it better

For 6C1 - you're picking one of 6 pieces

CNNNNN

So you have 6! total (6X5X4X3X2X1)
Divided by 5!(same Ns) & 1!(the one C)

6C2

CCNNNN = 6!/4!2! = 6X5/2 = 15

2C2 = 2!/2! = 1

Hope that's not too confusing.