Data Sufficiency

What is the face value of a 20 year insurance policy if the face value is fixed and the monthly premium is 0.03 percent of the face value?
(1) the monthly premium is $30
(2) the total amount to be paid in premium over the 20-year period is $7200

Last year the first $30,000 of each Country X resident's annual taxable income was taxed at the rate of 15%, and taxable income in excess of $30,000 was taxed at a rate of 27%. If Mr. Smith was a resident last year, was all of his taxable income taxed at the 15% rate?
(1) Last year Mr. Smith's tax, based on his taxable income, was $3750.
(2) If Mr. Smith's taxable income had been twice as much as it was, his tax would have been $9900.

jamesk486 wrote:What is the face value of a 20 year insurance policy if the face value is fixed and the monthly premium is 0.03 percent of the face value?
(1) the monthly premium is $30
(2) the total amount to be paid in premium over the 20-year period is $7200

The first statement says that the monthly premium is 30$ … so according to the given details .. 0.03*x/100=30 … where x is the face value … we can calculate x with this eqn .. so sufficient

The second statement says that in 20 yrs the total premium is 7200 .. so the monthly premium is 7200/(20*12) = 30 .. using the same eqn 0.03*x/100 = 30 .. we can find the value of x .. so sufficient .. so the answer is D

jamesk486 wrote: Last year the first $30,000 of each Country X resident's annual taxable income was taxed at the rate of 15%, and taxable income in excess of $30,000 was taxed at a rate of 27%. If Mr. Smith was a resident last year, was all of his taxable income taxed at the 15% rate?
(1) Last year Mr. Smith's tax, based on his taxable income, was $3750.
(2) If Mr. Smith's taxable income had been twice as much as it was, his tax would have been $9900.

According to the statement .. if the income is less than or equal to 30,000 .. then the tax will be 15% of that amt ..

Suppose the taxable income is x dollars above 30,000$ then the tax wuld be 15% of 30,000 + 27% of x …

.. so what the q basically asks is if the taxable income is greater than or less than 30,000$ ..

.. now the first statement says that his tax for last year was 3750 dollars .. if the tax is greater than 15% of 30,000 ( 4500 dollars ) then the income will be greater than 30,000 .. so according to the first statement mr. Smiths income was less than 30,000 ( bcoz the tax was 3750 $ ) … so the first statement is sufficient …

the second statement says that twice his tax = 9900 $ . so his tax is 9900/2 = 4950 $ … which is greater than 4500 so his income was taxed at both 15% and 27% .. basically it means that his income was more than 30,000 .. so sufficient .. so the answer is D ...

Hi Gabriel

Though the answer is D for the second question, I think you need to re-evaluate your interpretation of second statement.

It says " twice the taxable income" and not " twice the tax"

Answer should be D for both....for the second question...

Total tax = 9900
Tax for the first 30,000 = 4500
9900 - 4500 = 5400
5400 = 27% of x ; x = 20,000
So income = 20,000 + 30,000 = 50,000 when tax is 9900
So actual income would be 25,000
Statement II sufficient

Statement I is visibly sufficient