CHAPTER 12: NUMBERS AND PERCENTAGES

Misconceptions when dealing with Numbers and Percentages:

• Misconception #1: Increasing percentages automatically lead to increasing numbers:

  • If a percentage becomes larger, the number that corresponds to that percentage must also get larger.

  • This is not necessarily true because the overall size of the group under discussion could get smaller

  • If the overall total remains constant, an increasing percentage does translate into a larger number. But on the GMAT the size of the total is usually not given. If the percentage increases but the corresponding number decreases, then the overall total must have decreased

• Misconception #2: Decreasing percentages automatically lead to decreasing numbers:

  • Just because the percentage decreases does not necessarily mean that the corresponding number must become smaller.

  • If the percentage decreases but the corresponding number increases, then the overall total must have increased

• Misconception #3: Increasing numbers automatically lead to increasing percentages:

  • If the number increases but the corresponding percentage decreases, then the overall total must have increased

• Misconception #4: Decreasing numbers automatically lead to decreasing percentages:

  • If the number decreases, but the corresponding number increases, then the overall total must have decreased

• Misconception #5: Large numbers automatically mean large percentages, and smaller numbers automatically mean small percentages

  • The size of a number does not reveal anything about the percentage that number represents unless you know something about the size of the overall total that number is drawn from

• Misconception #6: Large percentages automatically mean large numbers, and small percentages automatically mean small numbers

• Numerical situations normally hinge on three elements: an overall total, a number within that total, and a percentage within the total

• Without at least two elements present, you cannot make a definitive judgement about what is occurring with another element.

• When you are given just percentage information, you cannot make a judgement about numbers. Likewise, when you are given just numerical information you cannot make a judgement about percentages

• Words used to introduce numerical ideas:

  • Amount

  • Quantity

  • Sum

  • Total

  • Count

  • Tally

• Words used to introduce percentage ideas:

  • Percent

  • Proportion

  • Fraction

  • Ratio

  • Incidence

  • Likelihood

  • Probability

  • Segment

  • Share

• When GMAT makers uses phrases such as “more likely” or “less likely” they are telling you that the percentage chances are greater than 50% or less than 50% respectively

• If the stimulus contains percentage or proportion information only, avoid answers that contain hard numbers.

  • Eg stimulus sentence: “The car market share of company X declines this year”

  • Avoid answers which say: “Company X sold a smaller number of cars this year”

• If the stimulus contains only numerical information, avoid answers that contain percentage or proportion information

  • Eg stimulus sentence: “Company Y sold fewer computers this year”

  • Avoid answers which say “Company Y now has a lower share of the computer market”

• If the stimulus contains both percentage and numerical information, any answer choice that contains numbers, percentages, or both may be true

• To weaken or strengthen an argument containing numbers and percentages, look carefully for information about the total amount(s) - does the argument make an assumption based on one of the misconceptions discussed earlier?

• Averages appear in a variety of GMAT questions

• An Average is a composite number, and within the average there can be a significant degree of variation and no single entity need embody the exact characteristic of the average (the average weight of a 1 pound rock and a 99 pound rock is 50 pounds)

• Market operation includes supply and demand, production, pricing, and profit.

• Market share is simply the portion of a market that a company controls. The market share can be measured either in terms of revenues (sales) or units sold

• Because market share is a numbers and percentages concept, market share can change when factors in the market change.

  • A company can gain market share (percentage) if the market shrinks and they maintain a constant size, or if they grow in an unchanging market

  • A company losing market share does not mean that their sales decreased, only that they became a smaller entity in the market relative to the whole (for example, the market grew and they stayed the same size)

  • A company could lose sales and still gain market share if the overall market became smaller

• The total market share must always add up to 100%

CHAPTER REVIEW

• Makers of GMAT often prey upon several widely held misconceptions

  • Misconception #1: Increasing percentages automatically lead to increasing numbers

  • Misconception #2: Decreasing percentages automatically lead to decreasing numbers

  • Misconception #3: Increasing numbers automatically lead to increasing percentages

  • Misconception #4: Decreasing numbers automatically lead to decreasing percentages

  • Misconception #5: Large numbers automatically mean large percentages, and small numbers automatically mean small percentages

  • Misconception #6: Large percentages automatically mean large numbers, and small percentages automatically mean small numbers

• Words that introduce numerical ideas:

  • Amount

  • Quantity

  • Sum

  • Total

  • Count

  • Tally

• Words that introduce percentage ideas:

  • Percent

  • Proportion

  • Fraction

  • Ratio

  • Incidence

  • Likelihood

  • Probability

  • Segment

  • Share

• Use the following rules for Must Be True questions:

  • If the stimulus contains percentage or proportion information only, avoid answers that contain hard numbers

  • If the stimulus contains only numerical information, avoid answers that contain percentages or proportion information

  • If the stimulus contains both percentage and numerical information, any answer choice that contains numbers percentages, or both may be true

• Use the following general rules for Weaken and Strengthen questions:

  • To weaken or strengthen an argument containing numbers and percentages, look carefully for information about the total amount(s) - does the argument make an assumption based on one of the misconceptions discussed earlier?

• Market share is simply the portion of a market that a company controls. Market share can be measured in terms of revenue (sales) or units sold.

• Regardless of the size of a market, total market share must always add up to 100%