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Example: Let a,b,c,d be distinct prime numbers satisfying :

2a+3b+5c+7d=162
11a+7b+5c+4d=162

Given that abcd=k. Find the number of distinct values of k?
A) 0
B) 1
C) 2
D) 3
E) 4

How we go about this? We were told in school, that n variables need n equations, but we have n-2 here. A road-block? No, a call to think deeply. Just see how we can reduce variables or increase equations.

We subtract the two equations and get 9a+4b=3d => 4b=3(d-3a)

RHS is divisible by 3, so should be LHS and therefore b=3

put this in the initial equations, and we are sure the max value of a can be =7 (i leave it to u to figure out how, a hint: all prime numbers are distinct, and we have used 3, we are left with the two smallest as 2 and 5).

Back again 3a=d-4=>d=3a+4 gives us (a,d)=(5,19),(11,37).. but clealry the second set wont work, very large values. We found the set, just by using the constraint, all are distinct primes and 3 has been used.

so we have b=3,a=5 d=19, there is no further need to go as we need the no of values of k which will obviously be 1. But for the sake of completeness we can check c=2

Seems like a marathon, but no its a 3-4 minute problem, once you start doing what I want you to !

This example is credited to Sureshbala..  

Here is a link to the original post… http://mathematics-for-iit.learnhub.com/lesson/5728-prime-numbers

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A number is divisible by 2 if its last digit is also (i.e. 0,2,4,6 or 8).

A number is divisible by 3 if the sum of its digits is also. Example: 726: 7+2+6= 15, so 726 is divisible by 3.

A number is divisible by 4 if the last two digits are divisible by 4. Example : 19716. 16 is divisible by 4, so the given no is divisible by 4.

A number is divisible by 5 if the last digit is 5 or 0.

A number is by divisible by 7. Double the last digit and subtract it from the remaining leading truncated number. If the result is divisible by 7, then so was the original number. Example :

672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes

905 (Double 5 is 10, 90-10=80, and 80÷7=11 ³/₇) No

A number is divisble by 8 if the last 3 digits of the number are divisble by 8. Example: 127104. 104/8= 13. So 127104 is divisble by 8.

A number is divisble by 9 if the sum of the digits is divisible by 9. Example: 288 = 2 + 8 + 8 = 18 (is divisible by 9). 288/9 = 32.

Test for divisibility by 11. Subtract the last digit from the remaining leading truncated number. If the result is 0 or  divisible by 11, then so was the first number. Apply this rule over and over again as necessary. Example:

9009–> 900-9 = 891 –>89-1=88 –>8-8=11, so yes, 9009 is divisible by 11

132–> 13 -2 =11. So 132 is divisible by 11

OR

If you sum every second digit and then subtract all other digits and the answer is 0 or divisible by 11. Example:

1364 ((3+4) – (1+6) = 0) Yes

3729 ((7+9) – (3+2) = 11) Yes

25176 ((5+7) – (2+1+6) = 3) No

Test for divisibility by 13. Add four times the last digit to the remaining leading truncated number. If the result is divisible by 13, then so was the first number. Apply this rule over and over again as necessary.
Example: 50661–>5066+4=5070–>507+0=507–>50+28=78 and 78 is 6*13, so 50661 is divisible by 13.

Test for divisibility by 17. Subtract five times the last digit from the remaining leading truncated number. If the result is divisible by 17, then so was the first number. Apply this rule over and over again as necessary.
Example: 3978–>397-5*8=357–>35-5*7=0. So 3978 is divisible by 17.

Test for divisibility by 19. Add two times the last digit to the remaining leading truncated number. If the result is divisible by 19, then so was the first number. Apply this rule over and over again as necessary.
Example: 101156–>10115+2*6=10127–>1012+2*7=1026–>102+2*6=114 and 114=6*19, so 101156 is divisible by 19.

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1) A Qualified Institutional Placement (QIP) is issued by an  indian company to raise capital to a selected group of shareholders, in exchange for equity.Its a private placement and not issued publicly. It was introduced byce the  the SEBI to reduce the dependance on foreign capital.

2) Global Depository Receipts( GDR) : A bank certificate issued in more than one country for shares in a foreign company. The shares are held by a foreign branch of an international bank. The shares trade as domestic shares, but are offered for sale globally through the various bank branches.

3) Fiscal Deficit: When a government’s total expenditures exceed the revenue that it generates (excluding money from borrowings). Deficit differs from debt, which is an accumulation of yearly deficits.

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There is a tough job awaiting the finance minister Pranab Mukherjee. He has to devise a budget plan, that would cater to all the  sections ranging from the corporates to the poorer sections of the society, or else the markets would react negatively. He has to raise money by divesting stake in the PSU’s , and has to concentrate on health, infrastructure and education facilities.  More so, the emphasis will be on the rural areas because rural demand is indispensable to  robust  economic growth. The government will do so by many social schemes(as promised in the election manifesto), such as the NREGA( National Rural Employment Guarentee Act)  where each family is ensured 100 days of employment,  and the Food security Act according to which each family below the poverty line is given 25 kg of food, at Rs 3 per kg.

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The secret of a successful life is to enjoy every moment:- to see happiness in small things- the smile of a toddler, the serenity of the beach, a small gesture of love from a close one. The secret is to always find a reason to smile and spread the happiness around.

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If  you want to soar like an eagle ,learn the ways of an eagle.If you associate with achievers, you will become one. If

you associate with thinkers, you will become one. If  you associate with complainers, you will become one.

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Readers are leaders..so as and when we read new and interesting things we’ll post it here..if u share our interests, do share ur views so that we can look at all sides of the coin..

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well, hopefully only the first of many blogs that will make this site helpful for many and one. Hope to talk about anything and everything thats worth talking about in my life.

A place where me and my friends and family can speak their mind. Amen.

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