Find the greatest number that will divide 43, 91 and 183 so as to leav

Question

Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

A. 4
B. 7
C. 9
D. 13
E. 24

Ohbebby · Accepted Answer

The answer is 4 and how it is 4 is below,
 
We can represent any integer number in the form of: D*q + r.
 Where D is divisor, q is quotient, r is remainder.

so each number can be written accordingly:
43 = D*q1 + r1;
91 = D*q2 + r2;
183 = D*q3 + r3;

r1,r2 & r3 will be same in above three equations according to the question.
D is the value that we want to find out. which should be greatest.

On solving three equations we get:

D*(q2-q1)= (91-43)=48
 D*(q3-q2)= (183-91)=92
 D*(q3-q1)= (183-43)=140
It is obvious that q3>q2>q1
For the greatest value of D that divide each equation we take the HCF of 48,92,140

THEREFORE ANSWER IS 4.
  Please give kudos !!

PKN · Answer

Greatest number=HCF(91-43, 183-91, 183-43)=HCF(48, 92, 140)=4.

Ans. (A)

BrentGMATPrepNow · Answer

This question lends itself to  testing the answer choices 
Since we're looking for the  greatest  number, we'll start at E and work our way to A

E) 24
43 divided by 24 equals 1 with remainder 19
91 divided by 24 equals 3 with remainder 19
183 divided by 24 equals 7 with remainder 15 
We need the SAME remainder each time - ELIMINATE E

D) 13
43 divided by 13 equals 3 with remainder 4
91 divided by 13 equals 7 with remainder 0
We need the SAME remainder each time - ELIMINATE D

C) 9
43 divided by 9 equals 4 with remainder 7
91 divided by 9 equals 10 with remainder 1
We need the SAME remainder each time - ELIMINATE C

B) 7
43 divided by 7 equals 6 with remainder 1
91 divided by 7 equals 13 with remainder 0
We need the SAME remainder each time - ELIMINATE B

By the process of elimination, the correct answer is A

RELATED VIDEO 
 https://www.youtube.com/watch?v=XCxgIR042tE

alok019 · Answer

required no.=h.c.f of(91-43),(183-91) and (183-43)
=h.C.F OF 48,92 and 140=4 
hence A option is correct

gracie · Answer

91=pn+r
43=qn+r
subtracting,
48=n(p-q)
n must be 4 or 24
only 4 leaves same remainder with all three dividends
A

Gagoosh · Answer

could u please explain this mthod in detail? would much appreciate the help.

KarishmaB · Answer

You are looking for the greatest divisor so you are looking for HCF. Say it is H. Say the common remainder is R.

43 = Ha + R ... (I)
91 = Hb + R ... (II)
183 = Hc + R ... (III)

(II) - (I) 
48 = H(b - a)

(III) - (I)
140 = H(c - a)

So H has to be a factor of 48 (= 2^4*3) as well as 140 (= 2^2 * 5 * 7). So highest value of H can be 4 as of now. Considering equation (III) - (II) we might get that it can be 2 only, we don't know yet. But note that the options have only 4 and hence answer (A)

Alternatively, try out the options. 
If 4 is the divisor, remainders are 3, 3, 3 - Answer
If 7 is the divisor, remainders are 1, 0 - Not the answer
...

BrushMyQuant · Answer

We need to find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

A. 4 
43, 91, 183 each when divided by 4 gives 3 remainder =>   POSSIBLE

B. 7 
43 when divided by 7 gives 1 remainder
91 when divided by 7 gives 0 remainder =>   NOT POSSIBLE

C. 9
Sum of all digits of 43 = 4+3 = 7 => Remainder of 43 by 9 = Remainder of 7 by 9 = 7
Sum of all digits of 91 = 9+1 = 10 => Remainder of 91 by 9 = Remainder of 10 by 9 = 1 =>   NOT POSSIBLE

D. 13
43 when divided by 13 gives 4 remainder
91 when divided by 13 gives 0 remainder =>   NOT POSSIBLE

E. 24
43 when divided by 24 gives 19 remainder
91 when divided by 24 gives 19 remainder
183 when divided by 24 gives 15 remainder=>   NOT POSSIBLE

So,  Answer will be A 
Hope it helps!

Watch the following video to learn the Basics of Divisibility Rules

https://www.youtube.com/watch?v=D9ZWVUyvFvM

Watch the following video to learn the Basics of Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Find the greatest number that will divide 43, 91 and 183 so as to leav

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Find the greatest number that will divide 43, 91 and 183 so as to leav

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards