If 3A = 4B = 5C = 6D and A + B + C + D = 1026, find the values of A, B

Question

If 3A = 4B = 5C = 6D and A + B + C + D = 1026, find the values of A, B, C and D.

A. 171, 228, 285, 342 
B. 342, 285, 228, 171 
C. 180, 216, 270, 360
D. 360, 270, 216, 180 
E. None of these

globaldesi · Accepted Answer

If 3A = 4B = 5C = 6D and A + B + C + D = 1026, find the values of A, B, C and D.
Let 3A = 4B = 5C = 6D = K
so  A =\frac{ K}{3} 
 B=\frac{ K}{4} 
 C= \frac{K}{5} 
 D=\frac{ K}{6} 
NOW GIVEN
A + B + C + D = 1026
THUS 
 \frac{ K}{3} +\frac{ K}{4}+ \frac{ K}{5}+\frac{ K}{6} = 1026 
OR
 \frac{57K}{60 }= 1026 
Solve for K
where K = 1080
substitute back for each value
  A =\frac{ 1080}{3} = 360 
 B=\frac{ 1080}{4} = 270 
 C= \frac{1080}{5} = 216 
 D=\frac{ 1080}{6}= 180 
D matches all these and thus the answer

sarahfiqbal · Answer

I plugged in answer choices for this question.

I started with option C, just because.

From answer choice C, its given A= 180. Therefore, 3A = 3(180) = 540

From the equation given, 3A= 4B, therefore 4B = 540. Then B =540/4 = 135 ---> this is  not the same  value as what is given for option C for value B i.e. 180,  216 , 270, 360

I stopped progressing with option C.

Then I moved on to choice D.

It's given A= 360, therefore 3A = 3 (360) =1080

From the equation given, 3A= 4B, therefore 4B = 1080. Then B = 270 ---> this is  the same value  as what is given for option D for value B i.e. 360,  270 , 216, 180

I stop calculating and hit D as my answer.

freedom128 · Answer

3A = 4B = 5C = 6D and all the choices available are positive integers. So,

A = 4B/3 = 5C/3 = 2D.
**A=2D --> choices A and C are out.

3A/4 = B = 5C/4 = 6D/4
** 3A/4=B. A must be divisible by 4. --> choice B is eliminated.

Left with choice D. Let's plug in number:
1) 3A = 4B = 5C = 6D (OK!!)
3(360) = 4(270) = 5(216) = 6(180)
2) A + B + C + D = 1026 (OK!!)
360+270+216+180=1026

Final answer is (D)

Posted from my mobile device

ScottTargetTestPrep · Answer

Let’s express each of the variables in terms of D. We see that A = 6D/3 = 2D; B = 6D/4 = 3D/2; and C = 6D/5. Substituting these quantities in the second equation, we have:

2D + 3D/2 + 6D/5 + D = 1026

Multiplying the equation by 10, we have:

20E + 15D + 12D + 10D = 10,260

57D = 10,260

D = 180

So A = 2(180) = 360, B = 3(180)/2 = 270, and C = 6(180)/5 = 216.

Answer: D

Bambi2021 · Answer

The numbers must be in descending order as A is bigger than B etc. Only options B and D matches this.

Try with D:

3A = 4B
3*360 = 4*270

Answer is D.

Posted from my mobile device

GMATGuruNY · Answer

If 3A=4B=5C=6D=60, the following ratio is yielded:
 A:B:C:D = 20:15:12:10

Sum of the ratio in blue = 20+15+12+10 = 57
Since the actual sum = 1026, the multiplier for the ratio =  \frac{1026}{57} = \frac{342}{19} = \frac{9*38}{19} = 9*2 = 18

Thus:
A = 20*18 = 360
B = 15*18 = 270
C = 12:18 = 216
D = 10*18 = 180

D

mimishyu · Answer

1026
=A + B + C + D 
since 3A = 4B, we substitute A with (4/3B)
=(4/3B) + B + C + D
same as A, substitute B with 5/4C
=4/3 * 5/4 C + 5/4C + C + D
eliminate the same number 4 with denominator and numerator on the first term, thus it becomes
=5/3C + 5/4C + C + D
then in the last replace C with 6/5D
=5/3 * 6/5D + 5/4 * 6/5D + 6/5D + D
to simplify, eliminate the same number on the fraction
=6/3D + 6/4D + 6/5D + D
=6/3D + 6/4D + 6/5D + 6/6D 
the denominator are 3、4、5、6 respectively, now find the LCM for these four numbers
LCM(3, 4, 5, 6)= LCM(3, 2^2, 5, 2*3) = 2^2 * 3 * 5 =60
expand the fraction to make the denominator, which we set as 60, the same
=120/60D + 90/60D + 72/60D + 60/60D
=342/60D=1026
D= (60*1026)/342 =180 thus ans(D)

sagarrathee77 · Answer

I think this approach worked because the person who made question didnt spend time in making options, otherwise imagine all options were in perfect ratio as demanded in the question, then this approach would fail

If 3A = 4B = 5C = 6D and A + B + C + D = 1026, find the values of A, B

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

If 3A = 4B = 5C = 6D and A + B + C + D = 1026, find the values of A, B

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