GMAT Math Questions | Geometry #12

Length of the diagonal of a square | Rates | Speed Distance Time

This GMAT quant problem solving practice question is from Mensuration (Solid Geometry): Concept: Length of the diagonal of a square and elementary speed, distance, and time concepts. A medium difficulty GMAT 650 level question.

Question 12: The area of a square field is 24200 sq m. How long will a lady take to cross the field diagonally at the rate of 6.6 km/hr?

  1. 3 minutes
  2. 0.04 hours
  3. 2 minutes
  4. 2.4 minutes
  5. 2 minutes 40 seconds

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Explanatory Answer | GMAT Geometry

Step 1 to solving this GMAT Geometry Question: Compute the length of the diagonal of the square

Let 'a' meters be the length of a side of the square field.
Therefore, its area = a2 square meters. --- (1)
The length of the diagonal 'd' of a square whose side is 'a' meters = √2 a --- (2)

From (1) and (2), we can deduce that the square of the diagonal = d2 = 2a2 = 2(area of the square)
Or d = \\sqrt{2 \times area}) meters.
d = \\sqrt{2 \times 24200}) = \\sqrt{48400}) = 220 m.

Step 2 to solving this GMAT Geometry Question: Compute the time taken to cross the field

The time taken to cross a distance of 220 meters while traveling at 6.6 kmph = \\frac{\text{220 m}}{\text{6.6 kmph}})

Convert unit of speed from kmph to m/min

1 km = 1000 meters and 1 hour = 60 minutes.
So, 6.6 kmph = \\frac{\text{6.6 × 1000}}{\text{60}}) m/min = 110 m/min
∴ time taken = \\frac{\text{220 m}}{\text{110 m/min}}) = 2 minutes

Choice C is the correct answer.

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