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jimmy86
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If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 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 ?

Show Spoiler
84

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-integers-a-b-and-c-are-positive-a-b-5-2-and-a-c-128150.html

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If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 03 Apr 2011, 08:12
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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 ?

Show Spoiler
84
Show more

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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If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 03 Apr 2011, 10:07
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jimmy86
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 ?

Show Spoiler
84
Show more

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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If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 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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If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 03 Apr 2011, 22:09
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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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If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 04 Apr 2011, 01:26
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thanks everyone.... Specially liked Ian`s explanation....the answer is a lot simpler than i thought....
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If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 02 Feb 2013, 17:19
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fluke
jimmy86
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 ?

Show Spoiler
84

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.
Show more




--------------------------------------------------------------------------------------------------------------------------------------------

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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If integers a,b,c are positive and a/b= 5/2 and a/c=7/5 04 Feb 2013, 04:42
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ulabrevolution
fluke
jimmy86
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 ?

Show Spoiler
84

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.
Show more

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: the-integers-a-b-and-c-are-positive-a-b-5-2-and-a-c-128150.html

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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