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# On a map, 1/2 inch represents 100 miles. According to this map, how ma

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Math Expert
Joined: 02 Sep 2009
Posts: 60645
On a map, 1/2 inch represents 100 miles. According to this map, how ma  [#permalink]

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26 Apr 2019, 02:27
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On a map, 1/2 inch represents 100 miles. According to this map, how many miles is City X from City Y ?

(1) City X is 3 inches from City Y on the map.
(2) Cities X and Y are each 300 miles from City Z.

DS45602.01
OG2020 NEW QUESTION

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Re: On a map, 1/2 inch represents 100 miles. According to this map, how ma  [#permalink]

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26 Apr 2019, 04:26
Given, 0.5 inches = 100 miles, 1 inch = 200 miles

From S1:

X - Y = 3 inches
Distance = 3*200 = 600 miles.

From S2:

City X and Y are each 300 miles from city Z.
City Z can be the center for these two cities, then distance = 600 miles.
If city X and Y lie on the same side of city Z, then distance = 0.
Insufficient.

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Re: On a map, 1/2 inch represents 100 miles. According to this map, how ma  [#permalink]

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27 Apr 2019, 06:51
Bunuel wrote:
On a map, 1/2 inch represents 100 miles. According to this map, how many miles is City X from City Y ?

(1) City X is 3 inches from City Y on the map.
(2) Cities X and Y are each 300 miles from City Z.

DS45602.01
OG2020 NEW QUESTION

We know that $$\frac{1}{2} \ in'=100 \ mi$$, so $$1 \ in'=200 \ mi$$. The original question: How many miles is City X from City Y ?

1) We know that the distance between City X and Y is $$3 \ in'=3\cdot 200=600 \ mi$$. Thus, the answer to the original question is a unique value. $$\implies$$ Sufficient

2) We know that City X and Y are both 300 miles from City Z. If they are in the opposite directions from City Z, then their distance from each other is 600 miles. However, if they are not in the opposite directions from City Z, then their distance from each other is less than 600 miles. Thus, we can't get a unique value to answer the original question. $$\implies$$ Insufficient

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Re: On a map, 1/2 inch represents 100 miles. According to this map, how ma  [#permalink]

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27 Apr 2019, 06:59
Bunuel wrote:
On a map, 1/2 inch represents 100 miles. According to this map, how many miles is City X from City Y ?

(1) City X is 3 inches from City Y on the map.
(2) Cities X and Y are each 300 miles from City Z.

DS45602.01
OG2020 NEW QUESTION

given 1 inch - 200 miles
#1
city x from city y ; distance ; 3*200 ; 600 miles
sufficeint
#2
not sufficient city z info irrelavant
IMO A
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Re: On a map, 1/2 inch represents 100 miles. According to this map, how ma  [#permalink]

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06 May 2019, 20:18
1
Bunuel wrote:
On a map, 1/2 inch represents 100 miles. According to this map, how many miles is City X from City Y ?

(1) City X is 3 inches from City Y on the map.
(2) Cities X and Y are each 300 miles from City Z.

DS45602.01
OG2020 NEW QUESTION

Since 1/2 inch = 100 miles, 1 inch = 200 miles. If we know the number of inches between cities X and Y on the map, then we know the actual distance between cities X and Y.

Statement One Alone:

City X is 3 inches from City Y on the map.

Since City X is 3 inches from City Y on the map, City X is actually 600 miles from City Y.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

Cities X and Y are each 300 miles from City Z.

We know the distance between X and Z and the distance between Y and Z; however we don’t know how these cities are positioned relative to each other. For instance, if the three cities are on a line and Z is between X and Y, then the distance between X and Y is 600 miles. On the other hand, if the three cities are not on a line and the triangle formed by these three cities is an equilateral triangle, then the distance between X and Y is also 300 miles. Statement two alone is not sufficient to answer the question.

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Re: On a map, 1/2 inch represents 100 miles. According to this map, how ma  [#permalink]

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21 May 2019, 16:01
Hi All,

We're told that on a map, 1/2 inch represents 100 miles. We're asked - according to this map - how many miles is City X from City Y. This question is based around the idea of 'unit conversions' (which is really just basic Arithmetic. The prompt gives us the ratio of map-inches to miles (re: 1/2 inch = 100 miles, so 1 inch = 200 miles). Thus, to answer this question, we need to know how many inches apart the two cities are.

(1) City X is 3 inches from City Y on the map.

Fact 1 gives us exactly what we need to know to answer the question. 3 inches = 600 miles, so the cities are 600 miles apart.
Fact 1 is SUFFICIENT

(2) Cities X and Y are each 300 miles from City Z.

The information in Fact 2 essentially creates a circle with City Z in the center and City X and City Y a 'radius' of 300 miles away. As such, the distance between City X and City Y could as far as 600 miles (if they're on exact opposite radii from City Z) or right next to one another.
Fact 2 is INSUFFICIENT

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Re: On a map, 1/2 inch represents 100 miles. According to this map, how ma   [#permalink] 21 May 2019, 16:01
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