GMAT Club Olympics 2024 (Day 6): On the number line shown, the tick

Question

https://gmatclub.com/forum/download/file.php?id=82519 On the number line shown, the tick marks are equally spaced and the coordinates of points A and B are 7^12 and 7^13, respectively. Which of the following coordinates represent the two points that are 2.5 times as far from Point A as Point A is from Point B? A. -2*7^{13} and 16*7^{12} B. -2*7^{13} and 15*7^{12} C. -2*7^{13} and 10*7^{12} D. -2*7^{12} and 16*7^{12} E. -2*7^{12} and 15*7^{12} GMAT-Club-Forum-fvr040br.png

Bunuel · Accepted Answer

GMAT Club Official Explanation: Assuming the coordinate of A is a, then the coordinate of B, in terms of a, is 7a. Thus, the distance between the points is 7a - a = 6a. So, we are looking for the points which are 6a * 2.5 = 15a distance from a, so the points are at a - 15a = -14a and a + 15a = 16a. Substituting the actual value of a we get: -14a = -14 * 7^12 = -2 * 7^13 and 16a = 16 * 7^12. Answer: A. GMAT-Club-Forum-yp8i3vzg.png

jack5397 · Answer

IMO -A

Find the distance between point A and Point B

D = A-B
   = 7^13-7^12 = 6*7^12

Now we need to find the points which are 2.5 times away from Point A as the distance between A & B.

6*7^12 *2.5 =  15*7^12

|7^12 - x| =  15*7^12

Open the modulus on both the sides x>0 and x<0

7^12 - x =  15*7^12

x = -2 *7^13

AND 7^12 - x =  -15*7^12

x = 16*7^12

Hence A.

AthulSasi · Answer

Distance between A & B =  7^{13} - 7^{12} 
 = 7^{12}(7-1) 
 = 6 * 7^{12}

2.5 times the distance =   2.5 * 6 * 7^{12} 
=  15 * 7^{12}

Left point = A - 2.5 times distance
 = 7^{12} - 15 * 7^{12} 
 = 7^{12} (1-15) 
 = -14 * 7^{12} 
 = -2 * 7^{13}

Right point = A + 2.5 times distance
 = 7^{12} + 15 * 7^{12} 
 = 7^{12} (1+15) 
 = 16 * 7^{12}

Answer A

NIKKtheSolver33 · Answer

I found the right answer this way:
A=7^12; B=7^13

Distance A-B = 7^13 - 7^12 = 7^12 *(7-1) = 6*7^12
Distance x 2.5 = 15*7^12

Then we can assume one point will be bigger (at the right) of point A while one will be smalle (at the left) of point A.
7^12 + 15*7^12 = 7^12*(1+15) = 16*7^12
 7^12 - 15*7^12 = 7^12*(1-15) = -14*7^12 = -2*7*7^12 = -2*7^13
Therefore answer A is the right one.

GMAT Club Olympics 2024 (Day 6): On the number line shown, the tick

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

GMAT Club Olympics 2024 (Day 6): On the number line shown, the tick

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