DSST Business Mathematics common mistakes
DSST Business Mathematics · Understand the traps and how to avoid them.
When averaging a set of numbers that includes a zero or a negative (e.g., a net-income figure of -$200 in a five-month average), the candidate silently drops the zero or treats the negative as positive, producing an average that is too high.
Candidates memorize 'average = add up and divide by how many' but then mentally edit the list to 'the numbers that count.' Zeros feel like non-data and negatives feel like errors, so they get excluded or sign-flipped.
What to do instead
Before dividing, rewrite the full list on scratch paper exactly as given, including 0 and any minus signs. Count the entries by pointing at each one. Then compute the sum with signs intact and divide by that count. Sanity-check: if the data includes a negative, the average must be less than the average of the positive entries alone.
On a ratio or proportion problem (e.g., splitting a profit in a 3:5:7 ratio, or scaling a recipe), the candidate divides the total by the ratio number instead of by the sum of the ratio parts, or adds the parts but then applies them to the wrong base.
The candidate pattern-matches 'ratio' to 'divide,' and the visible numbers 3, 5, 7 look like the divisors. The step of forming the sum of parts (15) is invisible in the problem statement, so it gets skipped.
What to do instead
Always write the ratio as parts and immediately compute the total parts: 3+5+7=15. One part = total/15. Then multiply each share by one part and verify the shares sum back to the original total. If they don't, the base was wrong.
In simple interest, the candidate plugs the annual rate straight into a problem stated in months (e.g., 9 months at 8%) without converting time to years, or converts by dividing by 100 twice.
The formula I = Prt is memorized as a string, and 't' is filled with whatever number appears, so 9 goes in as t=9. The convention that t is in years is a units rule, not a formula rule, and units rules are the first thing forgotten under time pressure.
What to do instead
Before substituting, write the units next to every value: P in dollars, r as a decimal per year, t in years. Convert months to years by dividing by 12 (9/12 = 0.75) and days by 360 or 365 as the problem implies. Then check magnitude: 9 years of interest should be roughly 12 times 9 months of interest.
In compound interest, the candidate uses the simple-interest formula or forgets to divide the annual rate by the compounding frequency, so quarterly compounding at 6% is computed with r = 0.06 and n = 1 instead of r/n = 0.015 over 4 periods per year.
The simple formula is overlearned and the compound formula A = P(1 + r/n)^(nt) has two places where n must appear. Candidates remember 'raise to a power' but not that the rate must be de-annualized and the time re-expressed in periods.
What to do instead
Rewrite the formula with the substitutions spelled out: r/n = 0.06/4 = 0.015 per quarter; nt = 4 x years = number of quarters. Compute the periodic rate first, then the exponent, then the power. Cross-check with one period of simple interest on the same principal; the compound answer must exceed it.
On an annuity or sinking-fund problem, the candidate cannot tell whether the payment is made at the end (ordinary annuity) or the beginning (annuity due), and applies the ordinary-annuity formula to a 'beginning of each period' scenario without the extra (1 + i) factor.
Both cases use the same numbers and nearly the same formula, and the only distinguishing cue is a phrase like 'at the start of each quarter.' Candidates skim past that phrase because it looks like boilerplate.
What to do instead
Underline the timing phrase before touching the formula. If payments are at the beginning, multiply the ordinary-annuity result by (1 + i). Also identify what is being asked: future value of the payments, present value, or the payment itself, and pick the formula for that unknown rather than the first one recalled.
On a net-pay problem, the candidate subtracts only the obvious deductions (federal tax, FICA) and forgets that gross pay must first be built from hours x rate plus overtime at 1.5x, or forgets that some deductions are percentages of gross while others are fixed dollar amounts.
The problem presents a list of deductions that looks homogeneous, and the candidate applies one treatment to all of them. The overtime premium and the percent-versus-dollar distinction are buried in the wording.
What to do instead
Build a vertical pay stub: regular hours x rate, overtime hours x 1.5 x rate, gross pay, then each deduction labeled '% of gross' or 'flat $.' Compute percent deductions from gross, not from net, and subtract in order. Total the deductions and subtract once to get net pay.
On a markup or discount chain (a 40% markup followed by a 25% markdown), the candidate adds and subtracts the percentages to get a net 15% change instead of multiplying the factors 1.40 x 0.75 = 1.05.
Percent changes feel additive because the numbers look like they belong on the same number line. The candidate does not see that the second percentage is taken on a different base.
What to do instead
Convert every percent change to a multiplier (markup: 1 + rate; markdown: 1 - rate; discount: price x (1 - d)). Chain them by multiplication, never by addition. If asked for the net percent change, subtract 1 from the product and convert back to a percent.
On depreciation and net-worth problems, the candidate mixes straight-line and declining-balance methods, or computes annual depreciation but forgets to subtract accumulated depreciation from cost to get book value, or treats a liability as an asset in the net-worth tally.
Both methods start from cost minus salvage and both produce an annual figure, so the first step looks identical. Net worth adds a second trap: assets and liabilities are listed together and only the sign or label distinguishes them.
What to do instead
Write the method name at the top of the work. Straight-line: (cost - salvage)/life each year, book value = cost - accumulated. Declining balance: rate x current book value, recomputed each year. For net worth, make two columns, assets and liabilities, total each, and subtract liabilities from assets.
On corporate-securities and ownership-distribution items, the candidate confuses par value with market value, or computes a dividend per share without first dividing the total dividend pool by the number of shares outstanding, or ignores preferred dividends in arrears before paying common.
The words 'value,' 'dividend,' and 'share' each have several meanings in corporate finance, and the candidate latches onto the first meaning that comes to mind rather than the one the question specifies.
What to do instead
Before computing, label each given number: par value, market price, shares outstanding, total dividend, preferred rate. Pay preferred (including any arrears) first, then split the remainder among common shares. Dividend per share = that class's pool / that class's shares, and check that the pools sum to the total declared.
On stock or asset turnover, the candidate divides the wrong way (cost of goods sold / average inventory inverted to inventory / COGS) or uses ending inventory instead of average inventory, and reports the result without units.
Turnover is a ratio with a conventional numerator and denominator, and candidates remember 'turnover = something over something' without the order. Average inventory requires an extra averaging step that is easy to skip when only one inventory figure is given.
What to do instead
Write the definition with words: turnover = sales (or COGS) / average balance. Compute average balance as (beginning + ending)/2 whenever both are given. State the units in the answer ('times per year'), and sanity-check: a turnover of 6 means inventory is replaced about every 2 months.