GMAT Data Insights Puzzles – Hourglass Puzzle Challenge

Let’s continue our puzzles discussion today with another interesting hourglass puzzle – time measurement using an hourglass.

What is an Hourglass?

This is what it looks like:

Let’s see how.

Hourglass Puzzle 1 – To improve reasoning for GMAT Data Insights

Puzzle 1: A teacher of mathematics used an unconventional method to measure a 15-minute time limit for a test. He just used 7 and 11-minute hourglasses. During the whole time he turned the hourglasses only 3 times (turning both hourglasses at once counts as one flip).

Explain how the teacher measured 15 minutes.

Solution: We have a 7 min and an 11 min hourglass. So we can measure time in intervals of 7 min as well as in intervals of 11 mins. But how about this: if both hourglasses start together, at the end of 7 mins, we have 4 mins of sand leftover in the top bulb of the 11 min hourglass. So we can measure 4 mins of time.

Further, if we flip the 7 min hourglass at this time and let it flow for 4 mins, we will have 3 mins of sand leftover and hence can measure a 3 min time interval too and so on…

Now, let’s see how we will measure 15 mins using a 7 min and an 11 min hourglass.

Start both 7 min and 11 min hourglasses. After the top bulb of the 7 min hourglass is empty, flip it. At this time, we have 4 min worth of sand in the top bulb of the 11 min hourglass. When the top bulb of the 11 min hourglass is empty, the bottom bulb of 7 min hourglass has 4 mins worth of sand.

11 mins have passed till now.

Now simply flip the 7 min hourglass again and let it run for 4 mins.

This is how we measure 11 + 4 = 15 mins of time.

Let’s look at another one.

Hourglass Puzzle 2 – To improve reasoning for GMAT Data Insights

Puzzle 2: Having 2 hourglasses, a 7 minute one and a 4 minute one, how can you correctly time 9 minutes?

Solution: Now we need to measure 9 mins using two hourglasses of 7 min and 4 min. We need to measure a time interval of 9 mins.

Start both the hourglasses. After 4 mins pass, we have all sand of the top bulb of the 4 min hourglass in the lower bulb. Flip the 4 min hourglass. In the 7 min hourglass, there is 3 min worth of sand in the upper bulb.

After 3 mins, all sand from the 7 min hourglass will be in the lower bulb and 1 min worth of sand will be in the upper bulb of the 4 min hourglass.

This is when our 9 min interval will start.

The 1 min sand will flow out from the 4 min hourglass.

Flip the 4 min hourglass and let all sand flow out. This will take 4 mins.

Again, flip the 4 min hourglass and let all sand flow out. This will take another 4 mins.

In all, we have measured a 1 + 4 + 4 = 9 min interval.