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19 Feb 2024, 10:19
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78% (01:26) correct
22%
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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
19 Feb 2024, 10:24
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LamboWalker
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Hope it helps.
19 Feb 2024, 11:13
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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
