If x is the sum of the first 10 positive multiples of 3 and y is the

Question

If x is the sum of the first 10 positive multiples of 3 and y is the sum of the first 10 positive multiples of 2, which of the following is a factor of x – y?

A. 20
B. 35
C. 55
D. 75
E. 90

This is a  PS Butler Question

Check the links to other Butler Projects: 
 
   Data Sufficiency Butler 
   Critical Reasoning Butler  
   Sentence Correction Butler  
   Reading Comprehension Butler  
   Integrated Reasoning Butler

chetan2u · Answer

x=3+6+9+…..+30=3(1+2+3+….+10)
y=2+4+6+…..+20=2(1+2+3+….+10)

x-y= 3(1+2+3+….+10) - 2(1+2+3+….+10) = (1+2+3+….+10)
= \frac{10*11}{2}  =55

C

gmatophobia · Answer

As the numbers are equally spaced, the sum = mean * number of terms

Mean of 10 positive multiples of 3 =  \frac{15 + 18 }{ 2}  =  \frac{33}{2}

Mean of 10 positive multiples of 2 =  \frac{10 + 12 }{ 2}  =  \frac{22}{2}

Difference =  \frac{33 - 22}{ 2} * 10   = 11*5 = 55

Factor = 55

Option C

zaidi1212 · Answer

3(1+2+3...10)-2(1+2+3+..10) = 3*11*10/2 - 2*11*10/2 = 55

ScottTargetTestPrep · Answer

The sum the of the first 10 positive multiples of 3 is:

10 x (30 + 3)/2 = 10 x 33/2 = 5 x 33 = 165

The sum of the first 10 positive multiples of 2 is:

10 x (20 + 2)/2 = 10 x 11 = 110

Thus x - y = 165 - 110 = 55, and a factor of 55 is factor of 55.

Answer: C

If x is the sum of the first 10 positive multiples of 3 and y is the

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 x is the sum of the first 10 positive multiples of 3 and y is the

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