## Ratio, proportions

Expand Messages
• Hi all Kindly help me solve the following problem in the easiest way possible. A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of
Message 1 of 13 , Jul 17, 2011
Hi all

Kindly help me solve the following problem in the easiest way possible.

A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of the salaries of last yr to this yr, in the case of Anup and Bunty respectively,are 3:4 and 5:7. If this year, the difference in their salaries is Rs.1150, what is Bunty's salary this year?

choices:
a.3150
b.3350
c.3250
d.3050

Thanks and Regards
Sindhuja
• hey...here is the answer let, a1=salary of anup last year b1=salary of bunty last year a2=salary of anup this year b2=salary of bunty this year a1/b1=2/3,
Message 2 of 13 , Jul 22, 2011
let,
a1=salary of anup last year
b1=salary of bunty last year
a2=salary of anup this year
b2=salary of bunty this year

a1/b1=2/3,  therefore  a1=(2/3)*b1.......................(1);
a1/a2=3/4,  therefore  a1=(3/4)*a2........................(2);
b1/b2=5/7,  therefore  b1=(5/7)*b2......................(3);
b2-a2=1150;b2=a2+1150.....................................(4);

substitute (2) & (3) in (1) and get a2
substitute a2 in (4) you will get b2 =3150=ans ...option(a)...

it will look long steps...if u practice it will be very easy

Boobalan S,
M.Tech,Process Design Engineer,
+91-7598099662

From: sindhuja <sindhujaa_2004@...>
To: ascent4cat@yahoogroups.com
Sent: Sun, 17 July, 2011 9:22:05 PM
Subject: [2IIM CAT Prep] Ratio, proportions

Hi all

Kindly help me solve the following problem in the easiest way possible.

A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of the salaries of last yr to this yr, in the case of Anup and Bunty respectively,are 3:4 and 5:7. If this year, the difference in their salaries is Rs.1150, what is Bunty's salary this year?

choices:
a.3150
b.3350
c.3250
d.3050

Thanks and Regards
Sindhuja

• Fastest way is to check which number is divisible by 7, since Bunty s salary has 5:7. Only number divisible by 7 is 3150. Quick way to check test of
Message 3 of 13 , Jul 22, 2011
Fastest way is to check which number is divisible by 7, since Bunty's salary has 5:7. Only number divisible by 7 is 3150. Quick way to check test of divisibility by 7 for 4 digit numbers is multiply first 2 digits by 2 and add to last 2 digits. 31*2 + 50 = 112, further for 3 digits, 1*2+12=14, 1*3+4=7. I have an algorithm for n digits test of divisibility by 7. Anyway, since this is only divisible by 7 this has to be the answer. Further verifying, 5:7 is 2250:3150(450*5 and 450*7). So 3150-1150=2000. 3:4 is 1500:2000. And original ratio is 1500:2250 = 2:3. Hope this helps.
• Fastest way is to check which number is divisible by 7, since Bunty s salary has 5:7. Only number divisible by 7 is 3150. Quick way to check test of
Message 4 of 13 , Jul 22, 2011
Fastest way is to check which number is divisible by 7, since Bunty's salary has 5:7. Only number divisible by 7 is 3150. Quick way to check test of divisibility by 7 for 4 digit numbers is multiply first 2 digits by 2 and add to last 2 digits. 31*2 + 50 = 112, further for 3 digits, 1*2+12=14, 1*3+4=7. I have an algorithm for n digits test of divisibility by 7. Anyway, since this is only divisible by 7 this has to be the answer. Further verifying, 5:7 is 2250:3150(450*5 and 450*7). So 3150-1150=2000. 3:4 is 1500:2000. And original ratio is 1500:2250 = 2:3. Hope this helps.

--- In ascent4cat@yahoogroups.com, "sindhuja" <sindhujaa_2004@...> wrote:
>
> Hi all
>
> Kindly help me solve the following problem in the easiest way possible.
>
> A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of the salaries of last yr to this yr, in the case of Anup and Bunty respectively,are 3:4 and 5:7. If this year, the difference in their salaries is Rs.1150, what is Bunty's salary this year?
>
> choices:
> a.3150
> b.3350
> c.3250
> d.3050
>
> Thanks and Regards
> Sindhuja
>
• ... The answer will be a) 3150 In this the ans has to be a multple of 3,5 and 7 i.e. 105. Only one option satisfies this
Message 5 of 13 , Jul 22, 2011
--- In ascent4cat@yahoogroups.com, "sindhuja" <sindhujaa_2004@...> wrote:
>
> Hi all
>
> Kindly help me solve the following problem in the easiest way possible.
>
> A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of the salaries of last yr to this yr, in the case of Anup and Bunty respectively,are 3:4 and 5:7. If this year, the difference in their salaries is Rs.1150, what is Bunty's salary this year?
>
> choices:
> a.3150
> b.3350
> c.3250
> d.3050
>
>

The answer will be a) 3150
In this the ans has to be a multple of 3,5 and 7 i.e. 105. Only one option satisfies this
• Hi, A = 2x last year B = 3x last year A = 2x * 4 / 3 this year = 8x / 3 B = 3x * 7 / 5 this year = 21x / 5 Diff = (63x - 40x) / 15 = 1150 x = 1150 * 15 / 23 =
Message 6 of 13 , Jul 22, 2011
Hi,

A = 2x last year
B = 3x last year

A = 2x * 4 / 3 this year = 8x / 3
B = 3x * 7 / 5 this year = 21x / 5

Diff = (63x - 40x) / 15 = 1150

x = 1150 * 15 / 23 = 50 * 15 = 750

B's sal this year = 21 * 750 / 5 = 21 * 150 = Rs 3150

What is the official answer ...
--
Regards,
Naveenan
2IIM Mumbai

CAT 2012 Batch Starts July 31st

CAT 2011 Crash - Starting Aug 7 - Batch of 8 students.

Office: +91-80970-48484

On Sun, Jul 17, 2011 at 9:22 PM, sindhuja wrote:

Hi all

Kindly help me solve the following problem in the easiest way possible.

A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of the salaries of last yr to this yr, in the case of Anup and Bunty respectively,are 3:4 and 5:7. If this year, the difference in their salaries is Rs.1150, what is Bunty's salary this year?

choices:
a.3150
b.3350
c.3250
d.3050

Thanks and Regards
Sindhuja

• Hi all PFB the solution given by a person Regards sindhuja ________________________________ From: Rahil Sahu To:
Message 7 of 13 , Jul 22, 2011
Hi all

PFB the solution given by a person

Regards
sindhuja

From: Rahil Sahu <rahilsahu@...>
To: sindhujaa_2004@...
Sent: Fri, 22 July, 2011 10:56:03 AM
Subject: Re: [2IIM CAT Prep] Ratio, proportions

Assume
Anup - 2a, Bunty - 3a in 1st yr

2nd yr
Anup - 4x2a/3; Bunty - 7x3a/5

21a/5 - 8a/3 = 1150
Solve for a, you get a =750

Bunty in 2nd yr = 21a/5 = 3150

Rahil Sahu
Naval Architect
VEDAM Design & Techinal Consultancy Pvt. Ltd.

Ph - 91-22-6710 9192

From: sindhuja <sindhujaa_2004@...>
To: ascent4cat@yahoogroups.com
Sent: Sun, 17 July, 2011 9:22:05 PM
Subject: [2IIM CAT Prep] Ratio, proportions

Hi all

Kindly help me solve the following problem in the easiest way possible.

A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of the salaries of last yr to this yr, in the case of Anup and Bunty respectively,are 3:4 and 5:7. If this year, the difference in their salaries is Rs.1150, what is Bunty's salary this year?

choices:
a.3150
b.3350
c.3250
d.3050

Thanks and Regards
Sindhuja

• Hi thanks for the solution. @ all: PFB another solution for the same question Regards sindhuja ________________________________ From: boobalan bala
Message 8 of 13 , Jul 22, 2011
Hi

thanks for the solution.

@ all: PFB another solution for the same question

Regards
sindhuja

From: boobalan bala <boobalanprpc@...>
To: sindhujaa_2004@...
Sent: Fri, 22 July, 2011 2:12:12 PM
Subject: Fw: [2IIM CAT Prep] Ratio, proportions

Boobalan S,
M.Tech,Process Design Engineer,
+91-8688196956

----- Forwarded Message ----
From: boobalan bala <boobalanprpc@...>
To: ascent4cat@yahoogroups.com
Sent: Fri, 22 July, 2011 2:09:16 PM
Subject: Re: [2IIM CAT Prep] Ratio, proportions

let,
a1=salary of anup last year
b1=salary of bunty last year
a2=salary of anup this year
b2=salary of bunty this year

a1/b1=2/3,  therefore  a1=(2/3)*b1.......................(1);
a1/a2=3/4,  therefore  a1=(3/4)*a2........................(2);
b1/b2=5/7,  therefore  b1=(5/7)*b2......................(3);
b2-a2=1150;b2=a2+1150.....................................(4);

substitute (2) & (3) in (1) and get a2
substitute a2 in (4) you will get b2 =3150=ans ...option(a)...

it will look long steps...if u practice it will be very easy

Boobalan S,
M.Tech,Process Design Engineer,
+91-7598099662

From: sindhuja <sindhujaa_2004@...>
To: ascent4cat@yahoogroups.com
Sent: Sun, 17 July, 2011 9:22:05 PM
Subject: [2IIM CAT Prep] Ratio, proportions

Hi all

Kindly help me solve the following problem in the easiest way possible.

A year ago the salaries of Anup and Bunty were in the ratio 2:3. the ratio of the salaries of last yr to this yr, in the case of Anup and Bunty respectively,are 3:4 and 5:7. If this year, the difference in their salaries is Rs.1150, what is Bunty's salary this year?

choices:
a.3150
b.3350
c.3250
d.3050

Thanks and Regards
Sindhuja

• lets anup s last yr salary be 2x and bunty s last yr salary be 3x......let this yr salary of anup and bunty be a and b respectively........now (2x)/a=3/4
Message 9 of 13 , Aug 3, 2011
 lets anup's last yr salary be 2x and bunty's last yr salary be 3x......let this yr salary of anup and bunty be a and b respectively........now (2x)/a=3/4 ->(1)        (3x/b)=5/7 ->(2)then a=8x/3       b=21x/5  difference in dis yr salary ie a-b=1150(8x/3) - (21x/5)=1150solving we get x=750   then bunty's dis yr salary  is 21x/5  = 3150
• data sufficiency If N is a natural number then number of factors of N^2 is ... A. N has 12 factors. B. N^3 has 70 factors. pls ans with xplanation
Message 10 of 13 , Aug 16, 2011
data sufficiency
If N is a natural number then number of factors of N^2 is ...

A. N has 12 factors.
B. N^3 has 70 factors.

pls ans with xplanation
• N has 12 factors = N can be of the form p^11 or p*q^5 or p^2 * q^3. So, this is not sufficient N^3 has 70 factors 70 can be written as 70 * 1 = N^3 = p^69
Message 11 of 13 , Aug 16, 2011
N has 12 factors => N can be of the form p^11 or p*q^5 or p^2 * q^3. So, this is not sufficient
N^3 has 70 factors

70 can be written as
70 * 1 => N^3 = p^69 possible => N = p^ 23
35 * 2 => N^3 =  p^34 * q  Not possible as this cannot be a perfect cube
5 * 14 => N^3 =  p^4 * q^13 Not possible as this cannot be a perfect cube
7 * 10 => N^3 = p^6 * q ^ 9 Possible => N = P^2 * q^3

So, this alone is not sufficient.

Both combined together, we can say N has to be of the form p^2 * q^3 and therefore number of factors of N^2 can be found.

Good question, but to be honest I do not think CAT will ask a question even as tough as this.

Cheers,
Rajesh
2IIM

On Wed, Aug 17, 2011 at 4:38 AM, mohit gupta wrote:

data sufficiency
If N is a natural number then number of factors of N^2 is ...

A. N has 12 factors.
B. N^3 has 70 factors.

pls ans with xplanation

• dere r 6 letters and 6 addressed envelops... what is the proabability that exactly 3 are in wrong envelops..
Message 12 of 13 , Aug 18, 2011
dere r 6 letters and 6 addressed envelops...

what is the proabability that exactly 3 are in wrong envelops..

• I think it should be 2400.. because you take 3 letters at random which is 6C3 then you multiply by the number of ways each will go in so 6*5*4 6C3*6*5*4 = 2400
Message 13 of 13 , Aug 19, 2011
I think it should be 2400..
because you take 3 letters at random which is 6C3 then you multiply by the number of ways each will go in so 6*5*4
6C3*6*5*4 = 2400

From: mohit gupta <mohit_luvkush@...>
To: "ascent4cat@yahoogroups.com" <ascent4cat@yahoogroups.com>
Sent: Friday, August 19, 2011 1:11 AM
Subject: Re: [2IIM CAT Prep] Ratio, proportions

dere r 6 letters and 6 addressed envelops...

what is the proabability that exactly 3 are in wrong envelops..

Your message has been successfully submitted and would be delivered to recipients shortly.