24 Mathematics Practice Questions & Answers

1. 1. Solve each of the three problems below, then add the three answers together and round the SUM to the nearest whole number. (1) Add: 3,148.7 + 926.45 + 51.25 (2) Multiply: one-fourth x 5,129.6 (3) Divide: 9,417.6 by 24

   • A.5,802
   • B.5,800
   • C.5,801✓ Answer
   • D.none of the above

   Carry full decimals through every step and round only once, at the end. (1) 3,148.7 + 926.45 + 51.25 = 4,126.4. (2) one-fourth = .25, so .25 x 5,129.6 = 1,282.4. (3) 9,417.6 / 24 = 392.4. SUM = 4,126.4 + 1,282.4 + 392.4 = 5,801.2. The digit after the decimal point is 2, which is less than 5, so drop the decimals: 5,801. The trap is rounding each sub-answer first (4,126 + 1,282 + 392 = 5,800); rounding intermediate values discards the .4 from each part and loses a whole unit.

   Source: NYS Dept. of Civil Service, Entry-Level Account/Audit Clerical Series test guide — Arithmetic Computation, three-problem SUM format and stated rounding rule (digit after the decimal point: below 5 round down, 5 or above round up); round only the final SUMReport a problem with this question

2. 2. Solve each of the three problems below, add the three answers together, then divide the SUM by three to find the AVERAGE and round to the nearest whole number. (1) Multiply: 1,842.5 x 3.2 (2) Add: 15,750.75 + 2,408.6 + 91.35 (3) Divide: 8,064 by 12

   • A.24,819
   • B.8,273✓ Answer
   • C.8,272
   • D.8,274

   (1) 1,842.5 x 3.2 = 5,896.0. (2) 15,750.75 + 2,408.6 + 91.35 = 18,250.70. (3) 8,064 / 12 = 672. SUM = 5,896.0 + 18,250.70 + 672 = 24,818.70. AVERAGE = 24,818.70 / 3 = 8,272.90. The digit after the decimal point is 9, which is 5 or more, so round up to 8,273. Choice 24,819 is the SUM rounded but never divided, and 8,272 comes from truncating the decimals instead of applying the rounding rule.

   Source: NYS Dept. of Civil Service, Higher Level Account Clerical Series test guide — Arithmetic Computation, AVERAGE variant (SUM divided by three, rounded to the nearest whole number)Report a problem with this question

3. 3. Solve each of the three problems below, add the three answers together to get the SUM, then find 28% of the SUM and round to the nearest whole number. (1) Add: 2,560.4 + 813.75 + 46.9 (2) Multiply: one-half x 4,820.6 (3) Divide: 7,392 by 16

   • A.6,293
   • B.4,531
   • C.1,762✓ Answer
   • D.1,763

   A percent must be converted to a decimal before multiplying: 28% = 0.28. (1) 2,560.4 + 813.75 + 46.9 = 3,421.05. (2) one-half = .5, so .5 x 4,820.6 = 2,410.30. (3) 7,392 / 16 = 462. SUM = 3,421.05 + 2,410.30 + 462 = 6,293.35. Then 0.28 x 6,293.35 = 1,762.138, and the digit after the decimal point is 1, so drop the decimals: 1,762. Choice 4,531 is 72% of the SUM (the complement, taken by mistake) and 6,293 is the SUM with no percent applied at all.

   Source: NYS Dept. of Civil Service, Higher Level Account Clerical Series test guide — Arithmetic Computation, PERCENT-of-SUM variant (stated percent of the SUM, rounded to the nearest whole number)Report a problem with this question

4. 4. Add the following three figures from a supply ledger and select the choice that matches your answer: 87,046.5 + 6,318.27 + 94,725.6

   • A.none of the above✓ Answer
   • B.187,090.37
   • C.198,090.37
   • D.188,009.37

   Align the decimal points and add: 87,046.5 + 6,318.27 = 93,364.77, and 93,364.77 + 94,725.6 = 188,090.37. That value appears in none of the three numeric choices, so 'none of the above' is correct. This is exactly why the option must be treated as live rather than as filler: 188,009.37 is a digit transposition of the true answer (90 written as 09), 187,090.37 is off by 1,000 in the thousands column, and 198,090.37 is off by 10,000 — each is a near-miss engineered to look right to someone who assumes a listed number must be the answer.

   Source: NYS Dept. of Civil Service clerical test guides — Arithmetic Computation instruction: select the choice that matches your answer, or, if no choice matches, select 'none of the above'Report a problem with this question

5. 5. A records unit holds 420 case files. Exactly 15% of the files are marked confidential. How many of the case files are NOT marked confidential?

   • A.405
   • B.357✓ Answer
   • C.85
   • D.63

   The question asks for the group that is left over, so take the complement of the percent before multiplying: 100% - 15% = 85%, and 85% = 0.85. Then 420 x 0.85 = 357. Each distractor is a documented error path: 63 is 420 x 0.15, the answer for the wrong group; 85 is the leftover percent mistaken for a count of files; and 405 comes from subtracting 15 from 420, treating a percent as if it were a quantity of files.

   Source: NYS Dept. of Civil Service clerical test guides — Arithmetic Reasoning, percent-complement sample pattern (solve 100% minus the stated percent, then multiply)Report a problem with this question

6. 6. An office spent $486.50 on printing last quarter. The supervisor budgets an amount 12% higher than that for next quarter. What is the budgeted amount for next quarter?

   • A.$558.40
   • B.$498.50
   • C.$544.88✓ Answer
   • D.$428.12

   A percent increase is applied to the original amount, so the new figure equals 100% + 12% = 112% of the old one: 486.50 x 1.12 = $544.88. Equivalently, the increase is 486.50 x 0.12 = $58.38, and 486.50 + 58.38 = $544.88. Choice $428.12 is 486.50 x 0.88, an 8-cent-perfect but direction-reversed answer (a 12% decrease), and $498.50 comes from adding $12 instead of 12 percent.

   Source: CalHR Office Technician (General) exam bulletin — Arithmetic Calculations, percent-increase-on-money item type (multiply the base by 1 plus the decimal form of the percent)Report a problem with this question

7. 7. A $9,600 annual maintenance charge is pro-rated among three departments in proportion to the floor space each occupies: Department A, 4,000 square feet; Department B, 3,500 square feet; Department C, 2,500 square feet. What is Department B's share of the charge?

   • A.$3,500.00
   • B.$2,400.00
   • C.$3,360.00✓ Answer
   • D.$3,200.00

   Pro-rating means each share is the same fraction of the total charge as that department's floor space is of the total floor space. Total space = 4,000 + 3,500 + 2,500 = 10,000 square feet, so Department B's share is 3,500 / 10,000 = 0.35, and 0.35 x $9,600 = $3,360.00. Choice $3,200.00 splits the charge evenly three ways, ignoring the proportion; $2,400.00 uses 25% instead of 35%; and $3,500.00 copies the square footage figure rather than computing a dollar share.

   Source: NYS Dept. of Civil Service, Higher Level Account Clerical Series test guide — Arithmetic Reasoning and Office Record Keeping: rate, ratio and proportion applied to allocating a total across unitsReport a problem with this question

8. 8. A clerk was assigned 240 benefit applications for the month and has finished processing 138 of them. What percent of the assigned applications has the clerk completed?

   • A.55.0%
   • B.none of the above
   • C.42.5%
   • D.57.5%✓ Answer

   A part is expressed as a percent of the whole by dividing the part by the base and multiplying by 100, and the base here is the full assignment of 240, not the remaining work. 138 / 240 = 0.575, and 0.575 x 100 = 57.5%. Choice 42.5% is the percent still outstanding (102 / 240), the complement taken by mistake; 55.0% is what results from rounding 138 down to 132 or otherwise using the wrong base.

   Source: CalHR Office Assistant (General) exam bulletin — Arithmetic Calculations: percent of a total, computed as part divided by the stated wholeReport a problem with this question

9. 9. A budget clerk lists six equipment requests received in one week: $812.40, $935.10, $678.90, $1,044.30, $756.30, and $862.50. What is the average (arithmetic mean) of the six requests?

   • A.$848.25✓ Answer
   • B.$1,017.90
   • C.none of the above
   • D.$5,089.50

   An arithmetic mean is the total of the values divided by how many values there are, so the divisor must be the count of items listed. Total = 812.40 + 935.10 + 678.90 + 1,044.30 + 756.30 + 862.50 = $5,089.50, and $5,089.50 / 6 = $848.25. Choice $5,089.50 is the total with no division performed at all, and $1,017.90 is the total divided by 5 — the miscount that happens when one line is skipped while adding.

   Source: CalHR Office Technician (General) exam bulletin — Arithmetic Calculations, averaging a listed column of dollar figures (sum divided by the number of entries)Report a problem with this question

10. 10. A maintenance log shows that 78 equipment repair calls were recorded over the course of one full year. Most nearly, what was the average number of repair calls per week? (Round to the nearest tenth.)

    • A.6.5
    • B.1.5✓ Answer
    • C.none of the above
    • D.1.3

    An average per period is the total divided by the number of periods, and the period asked about is the week, so the divisor is the 52 weeks in a year even though that number appears nowhere in the log. 78 / 52 = 1.5 calls per week. Choice 6.5 is 78 / 12, the average per month rather than per week, and 1.3 comes from dividing by 60 or otherwise misreading the divisor; picking the wrong divisor is the single most common error in per-period average items because the divisor comes from context, not from the data shown.

    Source: NYS Dept. of Civil Service clerical test guides — Record Keeping, 'most nearly' average-per-period item (total divided by the number of periods named in the question, rounded to the nearest tenth)Report a problem with this question

11. 11. Use the table below to answer this question. REASONS FOR DENIED RECORD REQUESTS Reason | Office A Number | Office A Percent | Office B Number | Office B Percent Incomplete form | 14 | 35% | 15 | 25% Missing identification | 6 | 15% | 24 | 40% Wrong office | 12 | 30% | 9 | 15% Fee unpaid | 8 | 20% | 12 | 20% Total | 40 | 100% | 60 | 100% For the two offices combined, which reason accounted for the largest number of denied requests?

    • A.Wrong office
    • B.Missing identification✓ Answer
    • C.Fee unpaid
    • D.Incomplete form

    Percentages in the two columns rest on different bases (40 requests in Office A, 60 in Office B), so they cannot be added or averaged across offices; only the raw counts can be combined. Adding the Number columns gives: incomplete form 14 + 15 = 29, missing identification 6 + 24 = 30, wrong office 12 + 9 = 21, fee unpaid 8 + 12 = 20. Missing identification is highest at 30. Adding the percent columns instead would give incomplete form 35 + 25 = 60 as the apparent winner, which is exactly the trap the two-base table is built to catch.

    Source: NYS Dept. of Civil Service clerical test guides — Understanding and Interpreting Tabular Material: percentages computed on different bases cannot be added or averaged across groups; combine raw countsReport a problem with this question

12. 12. Use the same table to answer this question. REASONS FOR DENIED RECORD REQUESTS Reason | Office A Number | Office A Percent | Office B Number | Office B Percent Incomplete form | 14 | 35% | 15 | 25% Missing identification | 6 | 15% | 24 | 40% Wrong office | 12 | 30% | 9 | 15% Fee unpaid | 8 | 20% | 12 | 20% Total | 40 | 100% | 60 | 100% Of all denied requests in the two offices combined, what percent were denied because of an incomplete form?

    • A.30%
    • B.29%✓ Answer
    • C.60%
    • D.35%

    A combined percent must be rebuilt from the combined raw counts over the combined base. Incomplete-form denials = 14 + 15 = 29, and the combined base = 40 + 60 = 100 requests, so 29 / 100 = 0.29 = 29%. Choice 30% is the simple average of 35% and 25%, which is invalid because the two percentages rest on unequal bases; 60% adds the two percentages outright; and 35% uses Office A's figure alone as if it applied to both offices.

    Source: NYS Dept. of Civil Service clerical test guides — Understanding and Interpreting Tabular Material: combining data sets requires recomputing a percent from summed counts over the summed baseReport a problem with this question

13. 13. A petty cash record is kept with a running balance. The opening balance was $4,820.00. The following entries were posted in order: receipt of $1,265.50; disbursement of $2,148.75; disbursement of $336.40; receipt of $892.15. What is the closing balance?

    • A.none of the above
    • B.$4,492.50✓ Answer
    • C.$9,462.80
    • D.$3,600.35

    In a running-balance record, receipts are added to the balance and disbursements are subtracted, and each new balance is carried forward as the starting point for the next line. $4,820.00 + $1,265.50 = $6,085.50; $6,085.50 - $2,148.75 = $3,936.75; $3,936.75 - $336.40 = $3,600.35; $3,600.35 + $892.15 = $4,492.50. Choice $9,462.80 treats every entry as an addition, and $3,600.35 is the balance after the third line, the answer of someone who stopped one row early.

    Source: NYS Dept. of Civil Service clerical test guides — Office Record Keeping: maintaining a record system using running balances (receipts added, disbursements subtracted, balance carried forward)Report a problem with this question

14. 14. A quarterly expense report lists four categories: postage $1,240; printing $3,480; supplies $2,180; equipment repair $1,100. Printing represents what percent of the grand total for the quarter?

    • A.34.8%
    • B.3.5%
    • C.56.5%
    • D.43.5%✓ Answer

    A line item's share is that line divided by the grand total, so the total must be computed before any percent is taken. Grand total = 1,240 + 3,480 + 2,180 + 1,100 = $8,000. Then 3,480 / 8,000 = 0.435, which is 43.5%. Choice 56.5% is the complement — everything except printing; 34.8% is a factor-of-ten slip in placing the decimal point; and 3.5% misplaces the decimal by two places.

    Source: NYS Dept. of Civil Service, Higher Level Account Clerical Series test guide — Office Record Keeping: completing a table summarizing data using totals, subtotals, averages and percentsReport a problem with this question

15. 15. A temporary clerk is paid a flat $156.00 for an assignment consisting of two shifts of 4 hours each. At the same hourly rate, how much would the clerk be paid for 22 hours of work?

    • A.$343.20
    • B.$429.00✓ Answer
    • C.$3,432.00
    • D.$19.50

    The setup requires three steps in order, because the hourly rate is not given and must be derived first. Step 1: total hours in the assignment = 2 shifts x 4 hours = 8 hours. Step 2: hourly rate = $156.00 / 8 = $19.50 per hour. Step 3: 22 hours x $19.50 = $429.00. Choice $19.50 is the intermediate rate, the answer of someone who stopped one step short; $3,432.00 multiplies the flat $156.00 by 22 without ever converting to an hourly rate.

    Source: CalHR Office Technician (General) exam bulletin — Arithmetic Calculations, multi-step rate problem (total hours, then hourly rate, then extended pay)Report a problem with this question

16. 16. Attendance at a public information counter was 260 visitors on Monday. Attendance tripled each day thereafter: Tuesday was three times Monday, Wednesday three times Tuesday, and so on. How many visitors were there on Thursday?

    • A.7,020✓ Answer
    • B.21,060
    • C.2,340
    • D.780

    Repeated tripling means multiplying by 3 once for each day after Monday, and Thursday is three days after Monday. Tuesday = 260 x 3 = 780; Wednesday = 780 x 3 = 2,340; Thursday = 2,340 x 3 = 7,020. Every wrong choice is a different day sitting in the answer set: 780 is Tuesday, 2,340 is Wednesday, and 21,060 is Friday. The classic error on growth items is an off-by-one on the number of days counted.

    Source: NYS Dept. of Civil Service clerical test guides — Arithmetic Reasoning: repeated-multiplication growth problem (apply the factor once per elapsed period named in the question)Report a problem with this question

17. 17. A supervisor must divide 1,462 blank forms as equally as possible among 7 clerks, giving each clerk the same whole number of forms. Any forms that cannot be divided evenly are returned to the storeroom. How many forms does each clerk receive, and how many are returned?

    • A.209 each, with 1 returned
    • B.209 each, with 6 returned
    • C.208 each, with 8 returned
    • D.208 each, with 6 returned✓ Answer

    Dividing a quantity evenly with a leftover calls for a whole-number quotient and a remainder, not a decimal answer. 1,462 / 7 = 208 with a remainder, since 7 x 208 = 1,456 and 1,462 - 1,456 = 6. So each clerk gets 208 forms and 6 are returned. Choice '209 each' is impossible because 7 x 209 = 1,463, one more form than exists; that is the check that catches a quotient rounded up instead of left whole.

    Source: NYS Dept. of Civil Service clerical test guides — Arithmetic Reasoning: division producing a whole-number quotient and remainder (verify by multiplying the quotient back against the divisor)Report a problem with this question

18. 18. Compute: (4 + 6)² x 3 - 58

    • A.242✓ Answer
    • B.300
    • C.54
    • D.none of the above

    The order of operations fixes the sequence: parentheses first, then the exponent, then multiplication, then subtraction. (4 + 6) = 10; 10² = 100; 100 x 3 = 300; 300 - 58 = 242. Choice 300 is the value one step early, before the subtraction is performed — the most common error on multi-step computation items. Choice 54 comes from squaring only the 6 instead of the quantity in parentheses: 4 + 36 x 3 - 58 = 54.

    Source: CalHR Office Technician (General) exam bulletin — Arithmetic Calculations, order-of-operations item (parentheses, exponents, multiplication/division, then addition/subtraction)Report a problem with this question

19. 19. Add the following fractions and express the result as a single fraction: 13/5 + 6/5

    • A.19/10
    • B.21/5
    • C.14/5
    • D.19/5✓ Answer

    When two fractions already share the same denominator, add the numerators straight across and leave the denominator unchanged, because the denominator names the size of the parts and that size does not change when parts are combined. 13 + 6 = 19, so the sum is 19/5. Choice 19/10 comes from adding the denominators as well, which would wrongly halve the size of each part; 14/5 and 21/5 come from mis-adding the numerators. The result is left as an improper fraction because nothing in the question asks for a mixed number.

    Source: CalHR Office Assistant (General) exam bulletin — Arithmetic Calculations, addition of fractions with a common denominator (add numerators, keep the denominator)Report a problem with this question

20. 20. Express the fraction 3/8 as a percent.

    • A.62.5%
    • B.38%
    • C.3.8%
    • D.37.5%✓ Answer

    To convert a fraction to a percent, divide the numerator by the denominator to get a decimal, then multiply by 100 because a percent is a rate per hundred. 3 / 8 = 0.375, and 0.375 x 100 = 37.5%. Choice 62.5% is 5/8, the complement of 3/8; 38% is a careless rounding that loses the exact half-percent; and 3.8% simply reads the digits of the fraction without dividing at all.

    Source: CalHR Office Assistant (General) exam bulletin — Arithmetic Calculations: converting among fractions, decimals and percents (divide, then multiply by 100)Report a problem with this question

21. 21. A photocopier produces 385 pages in 7 minutes. At that same rate, how many pages would it produce in 18 minutes?

    • A.770 pages
    • B.none of the above✓ Answer
    • C.1,100 pages
    • D.924 pages

    Find the unit rate first, then scale it to the new period: 385 pages / 7 minutes = 55 pages per minute, and 55 x 18 = 990 pages. Because 990 appears in none of the numeric choices, 'none of the above' is correct. Choice 770 is 55 x 14, the result of doubling the original 7 minutes instead of using 18; 1,100 is 55 x 20, an estimate that was never corrected back to the exact figure.

    Source: NYS Dept. of Civil Service clerical test guides — rate, ratio and proportion: derive the unit rate, then extrapolate to the period stated in the questionReport a problem with this question

22. 22. A public service counter opens at 9:45 a.m. and closes at 3:20 p.m. During that span it is closed to the public for a single 45-minute break. How much time is the counter actually open to the public?

    • A.4 hours 35 minutes
    • B.5 hours 35 minutes
    • C.6 hours 5 minutes
    • D.4 hours 50 minutes✓ Answer

    Elapsed time across noon is easiest on a 24-hour clock, which removes the a.m./p.m. off-by-one error: 3:20 p.m. is 15:20, so 15:20 - 9:45 = 5 hours 35 minutes total span. Subtracting the 45-minute closure gives 5 hours 35 minutes - 45 minutes = 4 hours 50 minutes open. Choice 5 hours 35 minutes is the full span with the break never deducted, and 6 hours 5 minutes is the classic hour-crossing error of borrowing incorrectly when the ending minutes are smaller than the starting minutes.

    Source: NYC DCAS clerical bridge exam task statement — performing ordinary mathematical computations, including elapsed time between two clock times spanning noonReport a problem with this question

23. 23. A shipment contains 24 identical cartons of letterhead. Each carton weighs 14 ounces. There are 16 ounces in one pound. What is the total weight of the shipment in pounds?

    • A.20 pounds 8 ounces
    • B.18 pounds
    • C.28 pounds
    • D.21 pounds✓ Answer

    Do the multiplication in the given unit first, then convert once at the end, using the conversion factor stated in the question. Total = 24 cartons x 14 ounces = 336 ounces, and 336 / 16 = 21 pounds exactly. Choice 28 pounds comes from dividing by 12 instead of 16 — importing the ounces-per-pound figure from a different conversion; the forgotten or wrong conversion factor is the standard error path on unit-conversion items.

    Source: CalHR Office Assistant (General) exam bulletin — Arithmetic Calculations: unit conversion for weight using the conversion factor supplied in the item (16 ounces = 1 pound)Report a problem with this question

24. 24. An office orders 45 reams of paper at $4.60 per ream. The vendor allows a 10% discount on the paper, and then adds a flat $18.00 delivery charge. What is the total amount of the invoice?

    • A.$204.30✓ Answer
    • B.$207.00
    • C.$225.00
    • D.$186.30

    Order matters on an invoice: the discount applies only to the merchandise, and the flat delivery charge is added after the discount because it is not part of the discounted goods. Merchandise = 45 x $4.60 = $207.00. Discount = $207.00 x 0.10 = $20.70, leaving $207.00 - $20.70 = $186.30. Invoice total = $186.30 + $18.00 = $204.30. Choice $186.30 stops before the delivery charge, $207.00 ignores the discount entirely, and $225.00 adds the delivery charge to the undiscounted merchandise.

    Source: NYS Dept. of Civil Service clerical test guides — Arithmetic Reasoning: multi-step invoice computation (extend unit price, apply the stated discount to merchandise only, then add flat charges)Report a problem with this question

Practice questions modeled on the common domains of civil service clerical-ability exams (grammar/spelling, math, filing, clerical accuracy). Not affiliated with or endorsed by any civil-service commission or testing vendor. Jurisdictions use different exams — check your announcement for its specific format. USAJOBS →