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.