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LamboWalker
Joined: 06 Jun 2021
Last visit: 06 Sep 2026
Posts: 238
GMAT Focus 1: 675 Q86 V81 DI83 
GMAT Focus 2: 735 Q90 V85 DI84 
GMAT 1: 690 Q48 V35
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Difficulty:
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Question Stats:
79% (01:26) correct
21%
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based on 204
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On the number line shown, the tick marks are equally spaced and the coordinates of points P and Q are \(2^1^7\) and \(2^1^8\), respectively. Which of the following points has the coordinate \(2^1^9\) ?
A. R
B. S
C. T
D. U
E. V
On the number line shown, the tick marks are equally spaced and the coordinates of points P and Q are \(2^1^7\) and \(2^1^8\), respectively. Which of the following points has the coordinate \(2^1^9\) ?
A. R
B. S
C. T
D. U
E. V
LamboWalker
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If P = 2^17 then Q = 2^17(2). So Q is twice the size of P, i.e., Q=2P.
We know the distance between two ticks equals the distance between P and Q. Taking the equation above, we can calculate that this distance is just equal to P, so 2^17: Q=2P ---> Q - P = P --> P = 2^17
We can rewrite 2^19 as 2^17(2^2) = 2^17(1+1+1+1). So we need to be 3 ticks away from 2^17 to be at 2^19. 3 ticks from P is S. IMO B
If P = 2^17 then Q = 2^17(2). So Q is twice the size of P, i.e., Q=2P.
We know the distance between two ticks equals the distance between P and Q. Taking the equation above, we can calculate that this distance is just equal to P, so 2^17: Q=2P ---> Q - P = P --> P = 2^17
We can rewrite 2^19 as 2^17(2^2) = 2^17(1+1+1+1). So we need to be 3 ticks away from 2^17 to be at 2^19. 3 ticks from P is S. IMO B
- For this problem we should attempt to find out two things:
Thing 1:
** What is 2^19 (in relation to point P) **
Ans --> 2^19 = 2^17*4
In-depth --> 2^17 * 2^2 --> 2^17 * 4 or 2 ^19
Thing 2:
** What is the difference between each point in the number line **
Ans --> Two points given, thus we can find the difference between Q and P
2^18 - 2^17 --> 2^17(2^1-1) --> 2^17(1) <-- This is the difference
Having Thing 1 and Thing 2 you should move on and try to find which point translates to [2^17 * 4]
- We found the difference (Thing 2) and we can apply that to each point
- Point R will be 2^18 + (1)2^17
- Point S will be 2^18 + 2*(1)*2^17 --> 2^17 * (2^1 + 2) --> 2^17 * 4
- So on so forth
With all this information we should be comfortable selecting Choice B!
In-depth: It may help to understand the mathematical principles behind these questions (Great information across the forum, try to look up theory on Number Properties (Evenly Spaced Sets), Simplifying Expressions(Exponents), or Tick Mark based questions).
Thing 1:
** What is 2^19 (in relation to point P) **
Ans --> 2^19 = 2^17*4
In-depth --> 2^17 * 2^2 --> 2^17 * 4 or 2 ^19
Thing 2:
** What is the difference between each point in the number line **
Ans --> Two points given, thus we can find the difference between Q and P
2^18 - 2^17 --> 2^17(2^1-1) --> 2^17(1) <-- This is the difference
Having Thing 1 and Thing 2 you should move on and try to find which point translates to [2^17 * 4]
- We found the difference (Thing 2) and we can apply that to each point
- Point R will be 2^18 + (1)2^17
- Point S will be 2^18 + 2*(1)*2^17 --> 2^17 * (2^1 + 2) --> 2^17 * 4
- So on so forth
With all this information we should be comfortable selecting Choice B!
In-depth: It may help to understand the mathematical principles behind these questions (Great information across the forum, try to look up theory on Number Properties (Evenly Spaced Sets), Simplifying Expressions(Exponents), or Tick Mark based questions).
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