Question

What is the ratio of insured adults in Urban : Rural areas?

• A. \(82:65\)
• B. \(748:477\)
• C. \(65:82\)
• D. \(477:748\)
• A. \(18.75%\)
• B. \(20.17%\)
• C. \(22.50%\)
• D. \(25.00%\)
• A. \(1,494\)
• B. \(1,560\)
• C. \(1,620\)
• D. \(1,650\)
• A. \(22,800\)
• B. \(23,100\)
• C. \(24,300\)
• D. \(25,200\)
• A. \(48.50%\)
• B. \(49.75%\)
• C. \(50.86%\)
• D. \(52.00%\)
• A. \(52.15%\)
• B. \(56.25%\)
• C. \(61.25%\)
• D. \(64%\)

Answer 1

The Correct Option is B

Step 1: Instead of adding Public, Private, and Employer directly, subtract the Uninsured share from 100% to get each area's insured share: Urban insured = \(100\% - 32\% = 68\%\), Rural insured = \(100\% - 47\% = 53\%\).
Step 2: Apply these to the actual populations: Urban insured = \(68\%\) of \(99{,}000 = 67{,}320\), Rural insured = \(53\%\) of \(81{,}000 = 42{,}930\).
Step 3: Divide both numbers by their greatest common factor, \(90\), to simplify: \(67{,}320 \div 90 = 748\), \(42{,}930 \div 90 = 477\).
\[ \boxed{748:477} \]

Answer 2

A unit-based approach avoids full multiplication: treat 1% of each population as a building block and scale up from there.

1. 82:65: One percent of Urban's population is 990, and one percent of Rural's is 810. Sixty-eight of Urban's percent-units and fifty-three of Rural's do not reduce anywhere close to 82:65, so this option is out.
2. 748:477: Urban insured is \(68 \times 990 = 67{,}320\) and Rural insured is \(53 \times 810 = 42{,}930\). Dividing each by 90 gives 748 and 477, matching this option precisely.
3. 65:82: This has Rural's insured figure listed as the larger of the two, but \(42{,}930\) is smaller than \(67{,}320\), so the order alone rules this out.
4. 477:748: Same issue as above in reverse; the smaller Rural figure needs to come second, not first, once the ratio is stated as Urban : Rural.

Scaling from 1% units for each area lands on the same 748:477 figure, with Urban ahead of Rural as the survey's insured counts require.

So the correct answer is 748:477.

Answer 3

Step 1: As a share of the entire 1,80,000 surveyed adults, Urban uninsured is \(32\% \times 55\% = 17.6\%\) and Rural uninsured is \(47\% \times 45\% = 21.15\%\).
Step 2: The gap between these whole-survey shares is \(21.15\% - 17.6\% = 3.55\) percentage points, which corresponds to \(3.55\%\) of \(1{,}80{,}000 = 6{,}390\) people.
Step 3: Express this gap as a percentage of Urban's own uninsured count: \(6{,}390 / 31{,}680 \times 100\).
\[ \boxed{20.17\%} \]

Answer 4

Rounding the raw numbers first gives a fast sanity check before committing to the exact figure.

1. 18.75%: This is exactly \(3/16\). Checking \(31{,}680 \times 3/16 = 5{,}940\), which is short of the actual gap of 6,390, so this fraction undershoots.
2. 20.17%: The gap of 6,390 divided by Urban's 31,680 is close to \(1/5\), or 20%, and the precise division refines that estimate to 20.17%, matching the rough fraction closely.
3. 22.50%: This is \(9/40\). Applying it, \(31{,}680 \times 9/40 = 7{,}128\), noticeably above the real gap of 6,390.
4. 25.00%: A quarter of 31,680 is 7,920, further still from the actual 6,390 gap.

Estimating the gap as roughly one-fifth of Urban's uninsured count, then refining, lands squarely on 20.17%.

So the correct answer is 20.17%.

Answer 5

Step 1: The population grows by 5% of 1,80,000, which is 9,000 extra people, split in the same 55:45 ratio as before: \(9{,}000 \times 0.55 = 4{,}950\) extra urban and \(9{,}000 \times 0.45 = 4{,}050\) extra rural.
Step 2: Apply each area's private-insurance rate only to its own extra population: extra Urban private = \(22\%\) of \(4{,}950 = 1{,}089\), extra Rural private = \(10\%\) of \(4{,}050 = 405\).
Step 3: Add the two contributions together.
\[ \boxed{1{,}089 + 405 = 1{,}494} \]

Answer 6

Splitting the extra 9,000 people by area first, then applying each area's own private-insurance rate, is a cleaner way to test the four options.

1. 1,494: The extra population breaks into 4,950 urban and 4,050 rural. Private coverage picks up \(22\%\) of the extra urban (1,089) and \(10\%\) of the extra rural (405), for a total of \(1{,}089+405=1{,}494\), matching this option.
2. 1,560: Reaching this number would require a private rate noticeably higher than 22% and 10% applied to the same extra population split, which is not what the passage states.
3. 1,620: This is even further from \(1{,}089+405\), requiring an inflated rate on one or both areas that the passage does not support.
4. 1,650: The largest of the four options, and the furthest from the actual extra-population calculation.

Applying the fixed private-insurance rates only to the newly added population, split by the same urban-rural ratio, gives exactly 1,494 additional privately insured people.

So the correct answer is 1,494.

Answer 7

Step 1: Urban's Public, Private, and Uninsured shares add to \(28\%+22\%+32\%=82\%\), leaving \(100\%-82\%=18\%\) for Employer, applied to 99,000 that is 17,820.
Step 2: Rural's Public, Private, and Uninsured shares add to \(35\%+10\%+47\%=92\%\), leaving \(8\%\) for Employer, applied to 81,000 that is 6,480.
Step 3: Add the two areas' Employer totals.
\[ \boxed{17{,}820+6{,}480=24{,}300} \]

Answer 8

Bounding the answer between Urban's Employer figure alone and the Rural figure implied by each option quickly narrows down the four choices.

1. 22,800: Urban Employer alone is already 17,820, so the Rural contribution here would need to be only 4,980, but \(8\%\) of 81,000 is 6,480, so this total is too low.
2. 23,100: This would need Rural's contribution to be 5,280, again below the actual 6,480 Rural figure, so it is also too low.
3. 24,300: Subtracting Urban's 17,820 leaves exactly 6,480 for Rural, which is precisely \(8\%\) of 81,000, confirming this total.
4. 25,200: This would require Rural's share to be 7,380, well above the actual \(8\%\) of 81,000, so this total overshoots.

Only 24,300 splits cleanly into Urban's 17,820 and Rural's 6,480 without contradicting either area's stated Employer rate.

So the correct answer is 24,300.

Answer 9

Step 1: Public insured (56,070) is close to half of total insured (1,10,250), since half of 1,10,250 is 55,125.
Step 2: Public exceeds this halfway mark by \(56{,}070-55{,}125=945\).
Step 3: Express this excess as a percentage of total insured and add it to the base 50%: \(945/1{,}10{,}250 \times 100 \approx 0.86\%\), so the share is \(50\%+0.86\%\).
\[ \boxed{50.86\%} \]

Answer 10

Since Public's own rate (28% Urban, 35% Rural) is lower than the overall insured rate (68% Urban, 53% Rural) in both areas, Public's share of insured people might seem like it should fall below 50%, and this can be sanity-checked before pinning down the exact figure.

1. 48.50%: This sits below the halfway mark, matching that rough expectation, but checking the exact counts (56,070 out of 1,10,250) shows the true share is actually a touch above half, so this undershoots.
2. 49.75%: Also just under half, and also below the true value once the exact counts are worked out.
3. 50.86%: The exact count of Public insured, 56,070, is slightly more than half of 1,10,250 total insured, because Rural leans on Public so heavily that it pulls the blended Public share above the 50% mark despite Public's rate being lower than the overall insured rate in each area individually.
4. 52.00%: This overstates how far above half the true share sits; the actual excess over 50% is under one percentage point, not two.

Rural's heavier reliance on Public coverage is exactly what tips the blended share just over half, landing on 50.86%.

So the correct answer is 50.86%.

Answer 11

Step 1: Blend each category's rate across both areas: Public = \(28\%\times55\%+35\%\times45\%=15.4\%+15.75\%=31.15\%\).
Step 2: Private = \(22\%\times55\%+10\%\times45\%=12.1\%+4.5\%=16.6\%\), and Employer = \(18\%\times55\%+8\%\times45\%=9.9\%+3.6\%=13.5\%\).
Step 3: Add the three blended categories together, since Insured is defined as Public plus Private plus Employer.
\[ \boxed{31.15\%+16.6\%+13.5\%=61.25\%} \]

Answer 12

Since Insured and Uninsured must add to 100% of the survey, testing each option's implied Uninsured share against the actual blended Uninsured rate confirms the answer.

1. 52.15%: This implies an Uninsured share of \(47.85\%\), well above the actual blended Uninsured rate of \(38.75\%\), so it is too low an Insured figure.
2. 56.25%: This implies Uninsured at \(43.75\%\), still higher than the true \(38.75\%\), so this Insured figure is also too low.
3. 61.25%: This implies Uninsured at exactly \(38.75\%\), matching the blended Uninsured rate computed from \(32\%\times55\%+47\%\times45\%=17.6\%+21.15\%=38.75\%\).
4. 64%: This implies Uninsured at only \(36\%\), below the true \(38.75\%\), so this Insured figure is too high.

Matching each option's implied Uninsured share against the actual blended rate of 38.75% confirms 61.25% as the correct Insured share.

So the correct answer is 61.25%.