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

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

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New post 15 Aug 2018, 04:01
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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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Re: If RS * KL = 1073 and SR * KL = 2117, find the value-Algebra-PS  [#permalink]

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New post 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.
B is the answer.
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If RS * KL = 1073 and SR * KL = 2117, find the value-Algebra-PS  [#permalink]

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New post 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.
B is the answer.


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

Thanking you in advance.
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Re: If RS * KL = 1073 and SR * KL = 2117, find the value-Algebra-PS  [#permalink]

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New post 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.
B is the answer.


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

Thanking you in advance.


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

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New post 15 Aug 2018, 08:59
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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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If RS * KL = 1073 and SR * KL = 2117, find the value-Algebra-PS  [#permalink]

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New post 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.
B is the answer.


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

Thanking you in advance.


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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Re: If RS * KL = 1073 and SR * KL = 2117, find the value-Algebra-PS  [#permalink]

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New post 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)
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PKN

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

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