The table below provides data on turtle nest counts at various Japanese beaches, showing specific counts from a past year and from 2013. Beach Year of Past Nest Count Past Nest Count 2013 Nest Count Prefecture Akabane 1992 29 39 Aichi Atsum 1996 19 50 Aichi Hiwasa 1979 76 18 Tokushima Inakahama 1986 540 2504 Kagoshima Itoman 1992 4 19 Okinawa Kujukuri 2004 15 39 Chiba Maehama 1989 611 1637 Okinawa Minaba Senri 1985 162 236 Wakayama Miyazaki 1985 607 1143 Miyazaki Nagahama 1997 106 612 Okinawa Ohgi & Shimonokae 1995 9 30 Okayama Okata 1991 19 37 Yamaguchi Shima Peninsula 2000 25 43 Mie Shingu 1989 15 15 Fukuoka Toyohashi 1995 30 20 Aichi For each of the following statements, select True if the statement can be verified to be true based on the information provided. Otherwise, select False .

1. Based on the table, exactly two prefectures did not experience an increase in nest counts from the past estimates to 2013. Here you have to be careful with prefectures, for example Aishi experienced a decrease at Toyohashi but it doesn't mean it didn't experience an increase (Akabane). Shingu and Hiwasa are the only beaches that don't increase (other than Toyohashi) and they belong to prefectures which only include them. So, this statement is true. 2. Based on the table, the greatest percentage increase in nest counts from past estimates to 2013 was approximately 600%. Let's look at the beaches with a more than 3x increase: Inakahama. 540 to 2504 means a 100 * \frac{2504 - 540}{540} \approx 364\% increase. Ohgi & Shimonokae. 9 to 30 means a 100 * \frac{30 - 9}{9} \approx 233\% increase. Nagahama. 106 to 612 means a 100 * \frac{612 - 106}{106} \approx 477\% increase. Itoman. 4 to 19 means a 100 * \frac{19 - 4}{4} = 375\% increase. The largest increase (477%) is less than 600%, so, this statement is false. 3. If the annual rate of increase at Maehama Beach remained constant from 1989 to 2013 and continues at the same rate until 2025, the estimated nest count in 2025 will exceed 2,400. From 1989 to 2013 Maehama Beach went from 611 to 1637 over 24 years, which is an increase in \frac{1637}{611} \approx 2.68 times or \sqrt {2.68} times per year on average. If the annual rate stayed the same until 2025, then the nest count will increase by (\sqrt {2.68})^{12} = \sqrt{2.68} \approx 1.64 times or from 1637 to 1637 * 1.64 \approx 2685 , which is more than 2400. So, the statement is true.

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The table below provides data on turtle nest counts at various Japanes

Bunuel

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Based on the table, exactly two prefectures, based on their total nest counts, did not experience an increase from past estimates to 2013.: True Based on the table, the greatest percentage increase in nest counts from past estimates to 2013 was approximately 600%.: False If the annual percentage rate of increase at Maehama Beach remained constant from 1989 to 2013 and continues at the same rate until 2025, the estimated nest count in 2025 will exceed 2,400.: True

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The table below provides data on turtle nest counts at various Japanese beaches, showing specific counts from a past year and from 2013.

Beach	Year of Past Nest Count	Past Nest Count	2013 Nest Count	Prefecture
Akabane	1992	29	39	Aichi
Atsum	1996	19	50	Aichi
Hiwasa	1979	76	18	Tokushima
Inakahama	1986	540	2504	Kagoshima
Itoman	1992	4	19	Okinawa
Kujukuri	2004	15	39	Chiba
Maehama	1989	611	1637	Okinawa
Minaba Senri	1985	162	236	Wakayama
Miyazaki	1985	607	1143	Miyazaki
Nagahama	1997	106	612	Okinawa
Ohgi & Shimonokae	1995	9	30	Okayama
Okata	1991	19	37	Yamaguchi
Shima Peninsula	2000	25	43	Mie
Shingu	1989	15	15	Fukuoka
Toyohashi	1995	30	20	Aichi

For each of the following statements, select True if the statement can be verified to be true based on the information provided. Otherwise, select False.

True	False	Statement
		Based on the table, exactly two prefectures, based on their total nest counts, did not experience an increase from past estimates to 2013.
		Based on the table, the greatest percentage increase in nest counts from past estimates to 2013 was approximately 600%.
		If the annual percentage rate of increase at Maehama Beach remained constant from 1989 to 2013 and continues at the same rate until 2025, the estimated nest count in 2025 will exceed 2,400.

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Bunuel

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26 Nov 2024, 06:19

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Bunuel

The table below provides data on turtle nest counts at various Japanese beaches, showing specific counts from a past year and from 2013.

Beach	Year of Past Nest Count	Past Nest Count	2013 Nest Count	Prefecture
Akabane	1992	29	39	Aichi
Atsum	1996	19	50	Aichi
Hiwasa	1979	76	18	Tokushima
Inakahama	1986	540	2504	Kagoshima
Itoman	1992	4	19	Okinawa
Kujukuri	2004	15	39	Chiba
Maehama	1989	611	1637	Okinawa
Minaba Senri	1985	162	236	Wakayama
Miyazaki	1985	607	1143	Miyazaki
Nagahama	1997	106	612	Okinawa
Ohgi & Shimonokae	1995	9	30	Okayama
Okata	1991	19	37	Yamaguchi
Shima Peninsula	2000	25	43	Mie
Shingu	1989	15	15	Fukuoka
Toyohashi	1995	30	20	Aichi

For each of the following statements, select True if the statement can be verified to be true based on the information provided. Otherwise, select False.

Official Solution:

Test one of the largest increases in the shortest period of time using the provided calculator. Nagahama beach had an initial estimate in 1997 of 106 nests and an estimate of 612 nests 17 years later for 2013. The total percent increase in that time was equal to (612 - 106) / 106 × 100 = 477%. That percentage divided by the 17 years would be approximately 34% per year.

Statement 1:

Based on the table, the prefectures that did not experience an increase in nest counts from past estimates to 2013 are:

• Tokushima (Hiwasa): Decreased from 76 to 18.

• Fukuoka (Shingu): Remained unchanged at 15.

Therefore, this statement is True.

Statement 2:

The greatest increase occurred at Nagahama Beach, where the nest count rose from 106 to 612, representing an increase of approximately six times, which corresponds to a 500% increase, not 600%. Therefore, this statement is False.

Statement 3:

From 1989 to 2013, the nest count at Maehama Beach increased from 611 to 1,637, corresponding to more than 2.5 times increase over 24 years: \(611*rate^{24} =1,637\). If the rate remains the same, in 12 years, the nest count becomes \(1,637*rate^{12}\). Since \(rate^{24} ≈ 2.5\), then \(rate^{12}=\sqrt{2.5}\). The square root of 2.5 is more than 1.5 (\(1.5^2 = 2.25\)), thus \(rate^{12} > 1.5\). This means that the nest count from 1,637 will increase by more than 50%, resulting in more than 2,400 nests in 2025.

Correct answer:

Based on the table, exactly two prefectures, based on their total nest counts, did not experience an increase from past estimates to 2013. "True"

Based on the table, the greatest percentage increase in nest counts from past estimates to 2013 was approximately 600%. "False"

If the annual rate of increase at Maehama Beach remained constant from 1989 to 2013 and continues at the same rate until 2025, the estimated nest count in 2025 will exceed 2,400. "True"

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Doesn't Toyohashi also reduce, from 30 to 20? Making the answer to this statement false?

Bunuel

The table below provides data on turtle nest counts at various Japanese beaches, showing specific counts from a past year and from 2013.

Beach	Year of Past Nest Count	Past Nest Count	2013 Nest Count	Prefecture
Akabane	1992	29	39	Aichi
Atsum	1996	19	50	Aichi
Hiwasa	1979	76	18	Tokushima
Inakahama	1986	540	2504	Kagoshima
Itoman	1992	4	19	Okinawa
Kujukuri	2004	15	39	Chiba
Maehama	1989	611	1637	Okinawa
Minaba Senri	1985	162	236	Wakayama
Miyazaki	1985	607	1143	Miyazaki
Nagahama	1997	106	612	Okinawa
Ohgi & Shimonokae	1995	9	30	Okayama
Okata	1991	19	37	Yamaguchi
Shima Peninsula	2000	25	43	Mie
Shingu	1989	15	15	Fukuoka
Toyohashi	1995	30	20	Aichi

For each of the following statements, select True if the statement can be verified to be true based on the information provided. Otherwise, select False.

Official Solution:

Test one of the largest increases in the shortest period of time using the provided calculator. Nagahama beach had an initial estimate in 1997 of 106 nests and an estimate of 612 nests 17 years later for 2013. The total percent increase in that time was equal to (612 - 106) / 106 × 100 = 477%. That percentage divided by the 17 years would be approximately 34% per year.

Statement 1:

Based on the table, the prefectures that did not experience an increase in nest counts from past estimates to 2013 are:

• Tokushima (Hiwasa): Decreased from 76 to 18.

• Fukuoka (Shingu): Remained unchanged at 15.

Therefore, this statement is True.

Statement 2:

The greatest increase occurred at Nagahama Beach, where the nest count rose from 106 to 612, representing an increase of approximately six times, which corresponds to a 500% increase, not 600%. Therefore, this statement is False.

Statement 3:

From 1989 to 2013, the nest count at Maehama Beach increased from 611 to 1,637, corresponding to more than 2.5 times increase over 24 years: \(611*rate^{24} =1,637\). If the rate remains the same, in 12 years, the nest count becomes \(1,637*rate^{12}\). Since \(rate^{24} ≈ 2.5\), then \(rate^{12}=\sqrt{2.5}\). The square root of 2.5 is more than 1.5 (\(1.5^2 = 2.25\)), thus \(rate^{12} > 1.5\). This means that the nest count from 1,637 will increase by more than 50%, resulting in more than 2,400 nests in 2025.

Correct answer:

Based on the table, exactly two prefectures did not experience an increase in nest counts from the past estimates to 2013. "True"

Based on the table, exactly two prefectures, based on their total nest counts, did not experience an increase from past estimates to 2013. "False"

If the annual rate of increase at Maehama Beach remained constant from 1989 to 2013 and continues at the same rate until 2025, the estimated nest count in 2025 will exceed 2,400. "True"

Bunuel

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26 Nov 2024, 11:05

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NishkarshS

Doesn't Toyohashi also reduce, from 30 to 20? Making the answer to this statement false?

Bunuel

The table below provides data on turtle nest counts at various Japanese beaches, showing specific counts from a past year and from 2013.

Beach	Year of Past Nest Count	Past Nest Count	2013 Nest Count	Prefecture
Akabane	1992	29	39	Aichi
Atsum	1996	19	50	Aichi
Hiwasa	1979	76	18	Tokushima
Inakahama	1986	540	2504	Kagoshima
Itoman	1992	4	19	Okinawa
Kujukuri	2004	15	39	Chiba
Maehama	1989	611	1637	Okinawa
Minaba Senri	1985	162	236	Wakayama
Miyazaki	1985	607	1143	Miyazaki
Nagahama	1997	106	612	Okinawa
Ohgi & Shimonokae	1995	9	30	Okayama
Okata	1991	19	37	Yamaguchi
Shima Peninsula	2000	25	43	Mie
Shingu	1989	15	15	Fukuoka
Toyohashi	1995	30	20	Aichi

For each of the following statements, select True if the statement can be verified to be true based on the information provided. Otherwise, select False.

Check the highlighted part. The statement talks about the prefectures, not beaches.

Based on the table, exactly two prefectures, based on their total nest counts, did not experience an increase from past estimates to 2013. "True"

Bismuth83

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26 Nov 2024, 11:22

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1. Based on the table, exactly two prefectures did not experience an increase in nest counts from the past estimates to 2013. Here you have to be careful with prefectures, for example Aishi experienced a decrease at Toyohashi but it doesn't mean it didn't experience an increase (Akabane). Shingu and Hiwasa are the only beaches that don't increase (other than Toyohashi) and they belong to prefectures which only include them. So, this statement is true.

2. Based on the table, the greatest percentage increase in nest counts from past estimates to 2013 was approximately 600%. Let's look at the beaches with a more than 3x increase:

Inakahama. 540 to 2504 means a \(100 * \frac{2504 - 540}{540} \approx 364\%\) increase.
Ohgi & Shimonokae. 9 to 30 means a \(100 * \frac{30 - 9}{9} \approx 233\%\) increase.
Nagahama. 106 to 612 means a \(100 * \frac{612 - 106}{106} \approx 477\%\) increase.
Itoman. 4 to 19 means a \(100 * \frac{19 - 4}{4} = 375\%\) increase.

The largest increase (477%) is less than 600%, so, this statement is false.

3. If the annual rate of increase at Maehama Beach remained constant from 1989 to 2013 and continues at the same rate until 2025, the estimated nest count in 2025 will exceed 2,400. From 1989 to 2013 Maehama Beach went from 611 to 1637 over 24 years, which is an increase in \(\frac{1637}{611} \approx 2.68\) times or \(\sqrt[24]{2.68}\) times per year on average. If the annual rate stayed the same until 2025, then the nest count will increase by \((\sqrt[24]{2.68})^{12} = \sqrt{2.68} \approx 1.64\) times or from 1637 to \(1637 * 1.64 \approx 2685\), which is more than 2400. So, the statement is true.

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In the Statement 3, the nest count was 1637 in 2013, and 611 in 1989, which is an increase of 1026 in 24 years. And, it is 12 years from 2013 to 2025, which means, at the same rate, the nest count should have been half of what it was during 1989-2013, that is 1026/2 = 513, and 1637+513, we will get 2150, and it is <2400.

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I think you made the mistake of using addition for the rate. Instead the annual rate is percent increase, for example: a 2% annual increase to 1000 is equal to 1000 * 1.02, and over 10 years it's \(1000 * (1.02)^{10}\).

chai9944

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Bunuel

The table below provides data on turtle nest counts at various Japanese beaches, showing specific counts from a past year and from 2013.

Beach	Year of Past Nest Count	Past Nest Count	2013 Nest Count	Prefecture
Akabane	1992	29	39	Aichi
Atsum	1996	19	50	Aichi
Hiwasa	1979	76	18	Tokushima
Inakahama	1986	540	2504	Kagoshima
Itoman	1992	4	19	Okinawa
Kujukuri	2004	15	39	Chiba
Maehama	1989	611	1637	Okinawa
Minaba Senri	1985	162	236	Wakayama
Miyazaki	1985	607	1143	Miyazaki
Nagahama	1997	106	612	Okinawa
Ohgi & Shimonokae	1995	9	30	Okayama
Okata	1991	19	37	Yamaguchi
Shima Peninsula	2000	25	43	Mie
Shingu	1989	15	15	Fukuoka
Toyohashi	1995	30	20	Aichi

For each of the following statements, select True if the statement can be verified to be true based on the information provided. Otherwise, select False.

But in the table there are three prefectures as such. Aichi is also a prefecture. Two of them gets decreased Hiwasa's Tokushima (76 to 18) and Toyohashi's Aichi (30 to 20) and one remains the same, Shingu's Fukuoka at 15. What am I missing? I am sure I have taken these from only prefectures.

Bunuel

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20 Jan 2025, 13:14

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Nivev

Bunuel

The table below provides data on turtle nest counts at various Japanese beaches, showing specific counts from a past year and from 2013.

Beach	Year of Past Nest Count	Past Nest Count	2013 Nest Count	Prefecture
Akabane	1992	29	39	Aichi
Atsum	1996	19	50	Aichi
Hiwasa	1979	76	18	Tokushima
Inakahama	1986	540	2504	Kagoshima
Itoman	1992	4	19	Okinawa
Kujukuri	2004	15	39	Chiba
Maehama	1989	611	1637	Okinawa
Minaba Senri	1985	162	236	Wakayama
Miyazaki	1985	607	1143	Miyazaki
Nagahama	1997	106	612	Okinawa
Ohgi & Shimonokae	1995	9	30	Okayama
Okata	1991	19	37	Yamaguchi
Shima Peninsula	2000	25	43	Mie
Shingu	1989	15	15	Fukuoka
Toyohashi	1995	30	20	Aichi

For each of the following statements, select True if the statement can be verified to be true based on the information provided. Otherwise, select False.

Statement 1: Based on the table, exactly two prefectures, based on their total nest counts, did not experience an increase from past estimates to 2013. "True"

There are three beaches in Aichi Prefecture: Akabane, Atsumi, and Toyohashi. While one of the beaches, Toyohashi, did not experience an increase in nest count from past estimates to 2013, the total nest count for the entire prefecture did show an increase.

This is why Aichi is not included in the count of prefectures with no increase.

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Hi Bunuel

In statement-3, to ease the calculation, can we also go ahead with the average rate method instead of compounding?
I wanted to check is it always safe to assume that question asks for compounded rate?

24 year (1989-2013) average annual rate = 100*((1637/611) - 1)/24 = ~7%
2013-2025 average rate = 7*12 = ~84%

2013 value (1637) will become ~3000 which is more than 2400

Bunuel

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Hi agrasan,

Great question! Let me address both parts — whether the average rate method works here, and whether it's always safe.

First, what the question actually means: When it says 'the annual percentage rate of increase remained constant,' that is GMAT-speak for compound growth — the same percentage applied each year to the growing base. So yes, the intended approach is compounding.

Here's the elegant compound method:
- Growth factor over 24 years (1989-2013): 1637/611 ≈ 2.678
- Since 2013-2025 is exactly 12 years = half of 24 years, the growth factor for the next 12 years is simply the square root: √2.678 ≈ 1.636
- 2025 estimate: 1637 × 1.636 ≈ 2,678 → exceeds 2,400 ✓

Now, your simple average method:
- You got ~7% per year, then applied 7% × 12 = 84%, giving ~3,000.
- The true compound rate is only about 4.1% per year (much lower than 7%).
- Your method overestimates because you're treating compound growth as linear. The simple average rate is always higher than the compound rate for the same total growth.

In THIS problem, both methods say 'exceeds 2,400,' so you got the right answer. But here's the danger: if the threshold were, say, 2,700, your method would say True (~3,000 > 2,700) while the correct compound method would say False (~2,678 < 2,700). So no, it is NOT always safe to use the average rate method.

Key Insight: On the GMAT, the compound approach has a beautiful shortcut here. Since 12 is half of 24, you just need the square root of the total growth factor. No need to find the annual rate at all!

Answer: True, False, True