Help on Free Quiz March 21

ya3sobi · Associate Joined: 01 Apr 2005 Posts: 2

Hi all,

any help with the following two questions.

Thanks in Advance Wink

3 The sum and product of three consecutive terms of an A.P. are 27 and 504 respectively. Which of the following could be the common difference of the terms of the A.P?
-3
3
-5
-4
6

5 Which of the following numbers will definitely divide a six digit positive integer xyxyxy, where x takes values between 1 and 9 and y takes values between 0 and 9?
39
28
35
41
93

ksb · Posted: Sat Apr 02, 2005 1:44 pm Post subject: answer to the second question

Any number of the form xyxyxy can be written as xy(10000) + xy(100) + xy

i.e, xy(10101)

Therefore, this number xyxyxy will be divisible by all divisors of 10101.

10101 = 111 * 91 = 37 * 3 * 13 * 7

Therefore, any combination of products of 2 or more of 37, 3, 13 and 7 will divide this number.

3 * 13 = 39.

Hence, choice A.

ya3sobi · Associate Joined: 01 Apr 2005 Posts: 2

Thanks a lot. Smile

mahe · Associate Joined: 15 Mar 2005 Posts: 2

Solution for Q5 by KSB was a good one.

Heres My approach though it fail to get right answer =>>>>

Anyone Remember Divisibility by 3 rule:
If the sum of the digits is divisible by three, the number is divisible by 3
add all the digits in xyxyxy we get 3(x+y).This is divisible by 3.

One can conclude that the divisor could also divisible by 3.
Now look at the choices only Options 1 and 5 are divisible.
So i eliminate other options.
39 = 3*13
93 = 3 * 31
Now its difficult which one to choose. ' Rolling Eyes

'

Intelligent Question setter (Choice setter) Cool

I would be grateful if someone extend this thought and solve this problem!!!!

Dan · Associate Joined: 22 Jan 2005 Posts: 3

amanthin · Posted: Sat Sep 24, 2005 11:18 pm Post subject:

Here is the answer to your first question...

Let the numbers be...
x x+d, x+2d
Staement 1: 3x+3d = 3(x+d) = 27
x+ d = 9
Statement 2:
x(x+d)(x+2d) = 504
x(9)(9+d) = 504 ... Substituting statement 1.
x(9+d) = 56
56 can be written as
14 * 4
28 * 2
Which would leave 9+d = 4 or 9+d = 2 ....
Therefore d could be -5 or -7...
So the answer is -5

shaji · Senior Consultant Joined: 25 Apr 2005 Posts: 34

amanthin · Posted: Mon Sep 26, 2005 10:51 pm Post subject:

Thanks for pointing that out Shaji. I should have made an explicit statement that you need to check the conditions before picking the answers. I was just showing how you could have multiple answers...