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If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 [#permalink]
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03 Apr 2011, 08:04
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Please post a simple solution for this question. I could do it by number picking strategy but then it takes a lot of time. Hello, I recently gave a CAT and there was a question for which the answer explanation was not very clear. If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 ,What is the smallest possible value of 2a+b ?OPEN DISCUSSION OF THIS QUESTION IS HERE: theintegersabandcarepositiveab52andac128150.html
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Re: PS : Algebra/Ratio  High Difficulty [#permalink]
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03 Apr 2011, 08:12
jimmy86 wrote: Please post a simple solution for this question. I could do it by number picking strategy but then it takes a lot of time. Hello, I recently gave a CAT and there was a question for which the answer explanation was not very clear. If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 ,What is the smallest possible value of 2a+b ?a/b= 5/2 2a=5b 1 a=(5/2)b a/c=7/5 5a=7c 5(5/2*b)=7c 25b=14c b is a multiple of 14 c is a multiple of 25. LCM of b and c = 350 25b=350 b=14 14c=350 c=25 5a=7c 5*a=7*25 a=35 2a+b = 2*35+14=84.
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Re: PS : Algebra/Ratio  High Difficulty [#permalink]
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03 Apr 2011, 10:07
jimmy86 wrote: Please post a simple solution for this question. I could do it by number picking strategy but then it takes a lot of time. Hello, I recently gave a CAT and there was a question for which the answer explanation was not very clear. If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 ,What is the smallest possible value of 2a+b ?When you have two positive integers a and b, and the ratio of a to b is 5 to 2, then a must always be a multiple of 5, and b must always be a multiple of 2. This will always be true when you have a ratio of two integers, provided the ratio is completely reduced (so if you knew, say, the ratio of a to b was 10 to 4, you'd need to reduce that ratio to 5 to 2 first before drawing any conclusions about multiples). So here, we know that the ratio of a to b is 5 to 2, so a is a multiple of 5. We also know the ratio of a to c is 7 to 5, so a is a multiple of 7. Thus a is a multiple of both 5 and 7, and the smallest possible value of a is 35. If a is 35, then since a/b = 5/2, b would be 14, and 2a + b = 84.
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Re: PS : Algebra/Ratio  High Difficulty [#permalink]
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03 Apr 2011, 19:02
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We can see that : a:b:c = 35:14:10 because a has 7 and 5 as factors, so least value of a = 35, and hence b = 14 ( and c = 25) So 2a + b = 70 + 14 = 84
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Re: PS : Algebra/Ratio  High Difficulty [#permalink]
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03 Apr 2011, 22:09
a:b = 5:2 a:c = 7:5 So to form a:b:c we a needs to be the LCM of 7 and 5 i.e. 35 So Multiply first ratio by 7 and second by 5 a:b:c = 35:14:25 So 2*35+14 = 84



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Re: PS : Algebra/Ratio  High Difficulty [#permalink]
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04 Apr 2011, 01:26
thanks everyone.... Specially liked Ian`s explanation....the answer is a lot simpler than i thought....
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Re: PS : Algebra/Ratio  High Difficulty [#permalink]
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02 Feb 2013, 17:19
fluke wrote: jimmy86 wrote: Please post a simple solution for this question. I could do it by number picking strategy but then it takes a lot of time. Hello, I recently gave a CAT and there was a question for which the answer explanation was not very clear. If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 ,What is the smallest possible value of 2a+b ?a/b= 5/2 2a=5b 1 a=(5/2)b a/c=7/5 5a=7c 5(5/2*b)=7c 25b=14c b is a multiple of 14 c is a multiple of 25. LCM of b and c = 350 25b=350 b=14 14c=350 c=25 5a=7c 5*a=7*25 a=35 2a+b = 2*35+14=84.  Hey Fluke, Can you please explain me where my method went wrong. a/b=5/2> a=2.5*b a/c=7/5>a=1.4*C 2.5*b = 1.4*c c=1.8*b As B and C have to be integers, the least integer value for B that would make C an integer is '5'. From the stem, we know that 2a=5b 2a+b=5b+b=6b As we know that b=5. 6b=30.



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Re: PS : Algebra/Ratio  High Difficulty [#permalink]
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04 Feb 2013, 04:42
ulabrevolution wrote: fluke wrote: jimmy86 wrote: Please post a simple solution for this question. I could do it by number picking strategy but then it takes a lot of time. Hello, I recently gave a CAT and there was a question for which the answer explanation was not very clear. If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 ,What is the smallest possible value of 2a+b ?a/b= 5/2 2a=5b 1 a=(5/2)b a/c=7/5 5a=7c 5(5/2*b)=7c 25b=14c b is a multiple of 14 c is a multiple of 25. LCM of b and c = 350 25b=350 b=14 14c=350 c=25 5a=7c 5*a=7*25 a=35 2a+b = 2*35+14=84.  Hey Fluke, Can you please explain me where my method went wrong. a/b=5/2> a=2.5*b a/c=7/5>a=1.4*C 2.5*b = 1.4*c c=1.8*bAs B and C have to be integers, the least integer value for B that would make C an integer is '5'. From the stem, we know that 2a=5b 2a+b=5b+b=6b As we know that b=5. 6b=30. From 2.5b=1.4c it follows that c=25/14*b. Now, 25/14 does not equal to 1.8. OPEN DISCUSSION OF THIS QUESTION IS HERE: theintegersabandcarepositiveab52andac128150.html
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Re: PS : Algebra/Ratio  High Difficulty
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