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If RS * KL = 1073 and SR * KL = 2117, find the value-Algebra-PS

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Director
Joined: 08 Jun 2013
Posts: 514
Location: India
GMAT 1: 200 Q1 V1
GPA: 3.82
WE: Engineering (Other)
If RS * KL = 1073 and SR * KL = 2117, find the value-Algebra-PS  [#permalink]

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15 Aug 2018, 04:01
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Difficulty:

35% (medium)

Question Stats:

94% (01:22) correct 6% (05:19) wrong based on 16 sessions

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If RS * KL = 1073 and SR * KL = 2117, find the value of (RS + KL) given that RS, SR and KL are all two digit positive integers.

A) 63
B) 66
C) 65
D) 95
E) 73

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Senior Manager
Joined: 18 Jul 2018
Posts: 484
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If RS * KL = 1073 and SR * KL = 2117, find the value-Algebra-PS  [#permalink]

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15 Aug 2018, 05:30
Factorizing 1073 gives RSxKL = 29x37.
Factorizing 2117 gives SRxKL = 29x73.
From both the equations, we get KL = 29, RS = 37 and SR = 73.
RS+KL = 29+37 = 66.
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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
If RS * KL = 1073 and SR * KL = 2117, find the value-Algebra-PS  [#permalink]

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15 Aug 2018, 08:46
Afc0892 wrote:
Factorizing 1073 gives RSxKL = 29x37.
Factorizing 2117 gives SRxKL = 29x73.
From both the equations, we get KL = 29, RS = 37 and SR = 73.
RS+KL = 29+37 = 66.

Hi Afc0892,
Request to explain the prime factorization of 1073 and 2117. How did you arrive at those factors?

_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Senior Manager
Joined: 18 Jul 2018
Posts: 484
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If RS * KL = 1073 and SR * KL = 2117, find the value-Algebra-PS  [#permalink]

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15 Aug 2018, 08:53
PKN wrote:
Afc0892 wrote:
Factorizing 1073 gives RSxKL = 29x37.
Factorizing 2117 gives SRxKL = 29x73.
From both the equations, we get KL = 29, RS = 37 and SR = 73.
RS+KL = 29+37 = 66.

Hi Afc0892,
Request to explain the prime factorization of 1073 and 2117. How did you arrive at those factors?

First, I did the prime factorizing of 1073. Took some crazy 2-3 minutes to do that. Once I arrived at this. The other prime factor was easy to find. Since one factor is common.
_________________

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Manager
Joined: 11 Mar 2018
Posts: 90
If RS * KL = 1073 and SR * KL = 2117, find the value-Algebra-PS  [#permalink]

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15 Aug 2018, 08:59
1
1
Harshgmat wrote:
If RS * KL = 1073 and SR * KL = 2117, find the value of (RS + KL) given that RS, SR and KL are all two digit positive integers.

A) 63
B) 66
C) 65
D) 95
E) 73

It may look a little complex but it actually is not (Atleast in my mind ). And I was able to solve it less than a minute. Here it goes...

Now we know, RS * KL = 1073;
So S * L will lead to 3.

so possible combos of S * L = 1 * 3 ---- 3 * 1 ---- 7 * 9 ---- 9 * 7
Now we need to have RS + KL, that is for S + L we can have 4 or 6 (from above highlighted part)
Hence if we see the answer choices. Only one matches ----- (B)

Option (B).

Hope it helps
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Director
Joined: 31 Jul 2017
Posts: 504
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
If RS * KL = 1073 and SR * KL = 2117, find the value-Algebra-PS  [#permalink]

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15 Aug 2018, 09:23
PKN wrote:
Afc0892 wrote:
Factorizing 1073 gives RSxKL = 29x37.
Factorizing 2117 gives SRxKL = 29x73.
From both the equations, we get KL = 29, RS = 37 and SR = 73.
RS+KL = 29+37 = 66.

Hi Afc0892,
Request to explain the prime factorization of 1073 and 2117. How did you arrive at those factors?

Its difficult to get these factors in real exam. I tried this way -

Let $$RS = ab, KL = cd$$ (Just for simplification purpose).

From the two equations -
$$cd*(ba-ab) = 1044$$
$$9*cd* (b-a) = 1044$$
$$cd *(b-a) = 29*4$$
Hence, $$cd = 29, ab = 37$$

Hence, $$(RS + KL) = 66$$
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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: If RS * KL = 1073 and SR * KL = 2117, find the value-Algebra-PS  [#permalink]

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15 Aug 2018, 10:04
Harshgmat wrote:
If RS * KL = 1073 and SR * KL = 2117, find the value of (RS + KL) given that RS, SR and KL are all two digit positive integers.

A) 63
B) 66
C) 65
D) 95
E) 73

Question stem:- RS+KL=?

Nearest perfect square term of 1073 is $$1089=33^2$$

So, 1073 can be written in the form: (a+b)(a-b)

$$1073=1089-16=33^2-4^2$$=(33+4)(33-4)=37*29

So, RS * KL =37*29-------------(1)
(RS=37 or, RS=29)

Given,
SR * KL = 2117
a) If RS=37,then SR=73. hence, $$KL=\frac{2117}{73}=29$$
b) If RS=73,then SR=37. hence, $$KL=\frac{2117}{37}$$, which yields non-integer value. (To be discarded)

So, RS=37 and KL=29

Therefore, RS+KL=37+29=66

Ans. (B)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Re: If RS * KL = 1073 and SR * KL = 2117, find the value-Algebra-PS &nbs [#permalink] 15 Aug 2018, 10:04
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