Latest Elitmus Aptitude Question SOLUTION: Abcd are four whole numbers such that a>b>c>d>0.the average of a &d is 7 and average of b & c is 4.5.how many such combinations are possible.

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Abcd are four whole numbers such that a>b>c>d>0.the average of a &d is 7 and average of b & c is 4.5.how many such combinations are possible.

Asked In Elitmus (11 years ago)

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RAKESH  (11 years ago)

a+d=14,b+c=9
(a,d)=(13,1),(12,2),(11,3),(10,4),(9,5),(8,6)
(b,c)=(8,1),(7,2),(6,3),(5,4)
a>b>c>d>0
13>7>2>1
13>6>3>1
13>5>4>1
12>6>3>2
12>5>4>2
11>5>4>3
so only 6 combinations.

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ANURAG MAHENDRU  (11 years ago)

b+c=9;
a+d=14;

1. 13>7>2>1
2. 13>6>3>1
3. 13>5>4>1
4. 12>6>3>2
5. 12>5>4>2
6. 11>5>4>3

Is this solution Helpfull? Yes (15) | No (2)  

Pallavi Chand  (11 years ago)

6 such combinations are possible.
since average of a and d is 7 so, a+d=14
average of b and c is 4.5 so, b+c=9;
possible values for b and c are 5,4; 6,3; 7;2
8,1 is not possible coz d cannot be equal to 0
taking values of a and d, where d=1, a=13 it is possible for all 3 cases before.
for d=2, a=12 it is not possible for last case where b=7, c=2 coz c!=d.
So it is possible for only 2 case
Similarly for d=3, a=11, it is only possible for case 1, where b=5, c=4.
So total of 3+2+1= 6 cases are possible.

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praveen  (11 years ago)

correct answer is 4
a+d/2 = 7
a+d=14
similarly
b+c=9
now apply we see that a is greatest and d is smallest and their sum is 14
so take a=13 and d=1
13+1=14 similarly take b=5 and c=4 5+4=9 this satisfies a>b>c>d>0
now
a=12 and d=12
12+2=14 similarly take b=6 and c=3 6+3=9 this satisfies a>b>c>d>0
and no other solution is possible so ans is 4.

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Anunay Singh  (11 years ago)

4 wasnt der in the options.. 3 6 8 n sumthing was the option...

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vikash kumar gupta  (11 years ago)

3 is the correct answer

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praveen  (11 years ago)

correct answer is 4
a+d/2 = 7
a+d=14
similarly
b+c=9
now apply we see that a is greatest and d is smallest and their sum is 14
so take a=13 and d=1
13+1=14 similarly take b=5 and c=4 5+4=9 this satisfies a>b>c>d>0
now
a=12 and d=2
12+2=14 similarly take b=6 and c=3 6+3=9 this satisfies a>b>c>d>0
and no other solution is possible so ans is 4.

Is this solution Helpfull? Yes (1) | No (3)  

Saifulwara Mallick  (11 years ago)

Though answer 4 is correct but explaination is not adequate.
Try to understand the question.
a,b,c,d are whole numbers greater than 0 where a>b>c>d>0.
Given, (a+d)/2=7
and (b+c)/2=4.5
With condition a>d and average = 7, the possibilities are..
a d avg
9 5 (9+5)/2=7
8 6 (8+6)/2=7
With condition b>c and average = 4.5, the possibilities are..
b c avg
8 1 (6+3)/2=4.5
7 2 (7+2)/2=4.5
6 3 (6+3)/2=4.5
5 4 (5+4)/2=4.5
Now...
keeping in mind a>b>c>d>0 , the possibilities of 4 digit number abcd are..
9851
9752
9653
8564
Therefore, only 4 possibilities.

Is this solution Helpfull? Yes (1) | No (3)  

N Arun Singh  (11 years ago)

go by options ..
since a+d=7*2(14) and b+c=(9)..

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nisha  (11 years ago)

wht is the procedure to solve this..

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satypal varma  (11 years ago)

13>6>3>1
12>5>4>2
11>5>4>3 a>b>c>d>0 only these three posbl soln

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sachin sharma  (11 years ago)

There can be five solutions
13>6>3>1
13>5>4>1
12>6>3>2
12>5>4>2
11>5>4>3

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