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There are two numbers a and b whose prod...

There are two numbers a and b whose product is 192 and the quotient of AM by HM of their greatest common divisor and least common multiple is `(169)/(48). The smaller of a and b is

A

2

B

4

C

6

D

12

Text Solution

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The correct Answer is:
B, D
If G=GED of a and b,L=LCM of a and b, we have `GL=ab=192 " " "……(i)"`
`(AM)/(HM)` of G and L is `((G+L)/(2))((G+L)/(2GL))=(169)/(48)`
`implies (G+L)^(2)=(169)/(12)GL=(169)/(12)GLxx192=13^(2)*4^(2)`
`G+L=52` but `GL=192`
`implies G=4,L=48 implies a=4,b=48` or `a=12,b=16`
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ARIHANT MATHS-SEQUENCES AND SERIES-Exercise (Questions Asked In Previous 13 Years Exam)
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  5. If a1, a2, a3,.....an are in H.P. and a1 a2+a2 a3+a3 a4+.......a(n-1...

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  6. Let V(r ) denotes the sum of the first r terms of an arithmetic progre...

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  7. Let Vr denote the sum of the first r terms of an arithmetic progressio...

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  8. Let V(r ) denotes the sum of the first r terms of an arithmetic progre...

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  9. LetA(1),G(1),H(1) denote the arithmetic, geometric and harmonic means ...

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  10. Let A1 , G1, H1denote the arithmetic, geometric and harmonic means re...

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  11. LetA(1),G(1),H(1) denote the arithmetic, geometric and harmonic means ...

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  12. In a G.P of positive terms if any term is equal to the sum of the next...

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  13. Suppose four distinct positive numbers a(1),a(2),a(3),a(4) are in G.P....

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  14. The first two terms of a geometric progression add up to 12. The sum o...

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  15. If the sum of first n terms of an A.P. is cn^(2) then the sum of squar...

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  16. The sum to infinity of the series 1+2/3+6/3^2+14/3^4+...is

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  17. Let Sk,k=1, 2, …. 100 denote the sum of the infinite geometric series ...

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  18. Let a1, a2, a3, ,a(11) be real numbers satisfying a1=15 , 27-2a2>0 an...

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  19. Check 2,4,6,8,10 are in A.P or not

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