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UGC NET PAPER 1 · UNIT 07 · MODULE 4: INTERPRETATION PRACTICE · TOPIC 8

Speed Tricks, Approximation and Common Traps

Fraction-percentage equivalents, approximation, shortcuts and the traps in option sets.

  • 10 sub-topics
  • 6 min read
  • Topic 8 of 11

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10 sub-topics, in the order to study them. Tap one to jump to it.

  1. §OverviewWith about two minutes per question and no calculator, speed comes from three habits: knowing fraction and percentage equivalents by heart, using simple decompositions (10…
  2. 8.1Fraction and percentage equivalents to memoriseFraction Per cent Fraction Per cent 1/2 50 1/9 11.11 1/3 33.33 1/10 10 1/4 25 1/11 9.09 1/5 20 1/12 8.33 1/6 16.67 1/15 6.67 1/7 14.28 1/16 6.25 1/8 12.5 1/20 5 Multiples…
  3. 8.2Percentage tricksCovers Swap trick, Build from 10 per cent, Use the fraction form, Increase and decrease by fractions, Percentage change by difference and more.
    • Swap trick
    • Build from 10 per cent
    • Use the fraction form
    • Odd percentages by splitting
  4. 8.3ApproximationIf the four options are well separated (differences of 5 to 10 per cent or more), round the numbers to the nearest convenient value and compute roughly.
  5. 8.4Comparing fractions and ratiosTo see which of two fractions is larger, cross-multiply.
  6. 8.5Average shortcutsUse an assumed mean : pick a convenient central number, add up the deviations from it, divide by the count and add the result back.
    • assumed mean
  7. 8.6Pie-chart shortcutsIf the question asks for a ratio or a comparison of two sectors, use the angles directly; you do not need the total.
  8. 8.7Table and graph reading shortcutsFor "highest growth", look first at columns with a small base; a small base with a moderate rise often gives the highest per cent. For "highest absolute increase", compare…
  9. 8.8Common traps and how option sets are builtWrong options in DI questions are usually not random: each one matches a specific mistake.
  10. 8.9Typical arrangement of the five questionsIn a set of five questions on one data display, a common arrangement (not a fixed rule) is: one direct-reading or total question, one average or ratio question, one…
  11. 8.10Practice routine for speedMemorise the fraction table above until you recall it without thinking. Time yourself: 5 questions on one data set in 8 minutes at first, then in 6 minutes. After each set…

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§Overview#

With about two minutes per question and no calculator, speed comes from three habits: knowing fraction and percentage equivalents by heart, using simple decompositions (10 per cent, 5 per cent, halves), and approximating when the options are far apart. This section collects the tricks that save the most time.

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8.1Fraction and percentage equivalents to memorise#

In brief

Fraction Per cent Fraction Per cent 1/2 50 1/9 11.11 1/3 33.33 1/10 10 1/4 25 1/11 9.09 1/5 20 1/12 8.33 1/6 16.67 1/15 6.67 1/7 14.28 1/16 6.25 1/8 12.5 1/20 5 Multiples…

Fraction Per cent Fraction Per cent
1/2 50 1/9 11.11
1/3 33.33 1/10 10
1/4 25 1/11 9.09
1/5 20 1/12 8.33
1/6 16.67 1/15 6.67
1/7 14.28 1/16 6.25
1/8 12.5 1/20 5

Multiples follow easily: 3/8 = 37.5 per cent, 5/8 = 62.5 per cent, 7/8 = 87.5 per cent, 2/3 = 66.67 per cent, 5/6 = 83.33 per cent.

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8.2Percentage tricks#

In brief

Covers Swap trick, Build from 10 per cent, Use the fraction form, Increase and decrease by fractions, Percentage change by difference and more.

  • Swap trick
  • Build from 10 per cent
  • Use the fraction form
  • Odd percentages by splitting

  1. Swap trick: x per cent of y equals y per cent of x. So 8 per cent of 25 is the same as 25 per cent of 8, which is 2.

  2. Build from 10 per cent: find 10 per cent by moving the decimal point, then add or halve. 15 per cent of 240 = 24 + 12 = 36. 5 per cent of 240 = 12. 25 per cent of 240 = 60.

  3. Use the fraction form: 12.5 per cent of 160 is 160 / 8 = 20; 33.33 per cent of 84 is 84 / 3 = 28; 16.67 per cent of 108 is 108 / 6 = 18.

  4. Increase and decrease by fractions: a 25 per cent increase multiplies by 5/4, so 80 becomes 100. A 20 per cent decrease multiplies by 4/5, so 150 becomes 120. A 50 per cent increase multiplies by 3/2.

  5. Percentage change by difference: find the difference first, then divide by the old value. From 180 to 225 the difference is 45 and 45 / 180 = 25 per cent.

  6. Odd percentages by splitting: 17 per cent of 300 = 10 per cent (30) + 7 per cent (21) = 51.

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8.3Approximation#

In brief

If the four options are well separated (differences of 5 to 10 per cent or more), round the numbers to the nearest convenient value and compute roughly.

If the four options are well separated (differences of 5 to 10 per cent or more), round the numbers to the nearest convenient value and compute roughly. For example, 487 out of 1,962 is close to 500 out of 2,000, which is 25 per cent; the true value is 24.8 per cent. Decimals such as 49.7 can be treated as 50. Do not approximate when options are close (for example 24.8, 25.1, 25.4), or when the question asks for a difference between nearly equal numbers, because rounding errors can exceed the gap.

After approximating, look at the options and eliminate by size and last digit before calculating further.

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8.4Comparing fractions and ratios#

In brief

To see which of two fractions is larger, cross-multiply.

To see which of two fractions is larger, cross-multiply. To compare 7/12 and 9/16: 7 × 16 = 112 and 9 × 12 = 108, so 7/12 is larger. For "which year had the highest per cent", do not calculate all years fully; round each ratio and compare the top two or three.

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8.5Average shortcuts#

In brief

Use an assumed mean : pick a convenient central number, add up the deviations from it, divide by the count and add the result back.

  • assumed mean

Use an assumed mean: pick a convenient central number, add up the deviations from it, divide by the count and add the result back. Marks 48, 52, 55, 45, 50: take 50 as the assumed mean; deviations are −2, +2, +5, −5, 0, which total 0, so the mean is 50. If the observations are in an evenly spaced series, the average equals the middle value (or the average of the two middle values).

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8.6Pie-chart shortcuts#

In brief

If the question asks for a ratio or a comparison of two sectors, use the angles directly; you do not need the total.

If the question asks for a ratio or a comparison of two sectors, use the angles directly; you do not need the total. If it asks for a value, convert the angle into a fraction of 360 (for example 90° = 1/4, 120° = 1/3, 45° = 1/8) and multiply by the total. Check that all the angles add up to 360° before using any of them.

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8.7Table and graph reading shortcuts#

In brief

For "highest growth", look first at columns with a small base; a small base with a moderate rise often gives the highest per cent. For "highest absolute increase", compare…

  • For "highest growth", look first at columns with a small base; a small base with a moderate rise often gives the highest per cent.

  • For "highest absolute increase", compare simple differences and ignore the base.

  • For a stacked bar chart, subtract the lower edge from the upper edge to find a segment.

  • For a line graph with two series, the vertical gap between the lines is the difference at that point.

  • If a graph has two y-axes (left and right), check which axis each series uses.

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8.8Common traps and how option sets are built#

In brief

Wrong options in DI questions are usually not random: each one matches a specific mistake.

Wrong options in DI questions are usually not random: each one matches a specific mistake. Knowing the mistakes helps you reject options quickly.

Trap Wrong approach Correct approach
Wrong base Dividing by the new value Divide by the old value
Points versus per cent Giving 5 when 25 per cent was asked Check the exact wording
Units Mixing thousands with lakhs or crores Read the headnote or axis title
Reverse ratio Giving B : A when A : B was asked Follow the order of the question
Wrong series Reading the girls' bar for boys Check the legend and colour key
Cumulative data Treating a running total as a yearly figure Read the graph title
Average of averages Averaging two group means without weights Use the weighted mean
Truncated axis Judging bar size by length alone Check whether the axis starts at zero
Pie with different totals Comparing shares across two pies Convert to absolute values first
Assuming a trend Extending a line beyond the data Answer only from the data shown
Increase equals decrease Believing +20 per cent then −20 per cent returns to the start Net change is −4 per cent
"Approximately" ignored Computing exactly and failing to match Pick the nearest option

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8.9Typical arrangement of the five questions#

In brief

In a set of five questions on one data display, a common arrangement (not a fixed rule) is: one direct-reading or total question, one average or ratio question, one…

In a set of five questions on one data display, a common arrangement (not a fixed rule) is: one direct-reading or total question, one average or ratio question, one percentage or percentage-change question, one comparison or maximum question, and one slightly longer question that combines two steps. Solve the easiest first, leave the two-step question for last, and use the time you save on the earlier ones.

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8.10Practice routine for speed#

In brief

Memorise the fraction table above until you recall it without thinking. Time yourself: 5 questions on one data set in 8 minutes at first, then in 6 minutes. After each set…

  • Memorise the fraction table above until you recall it without thinking.

  • Time yourself: 5 questions on one data set in 8 minutes at first, then in 6 minutes.

  • After each set, note which trap caught you, and keep a personal list of traps.

  • Practise approximating first, and exact calculation only when needed.

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