## How to find a percent of a number – without a calculator

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Difficulty level: Algebra Min/Max at the Sub-600 Level Obstacles Sets that cross each other Source: GMAT Prep Source: Official Guide Source: OG 10 Source: OG 11 Source: OG 12 Source: OG 2015 Source: OG 2016
In a workgroup of 50 researchers, 40% will be assigned to Team A, while the remaining 60% will be assigned to Team B. However, Team A is favored by 70% of the researchers, while Team B is preferred by 30%. What is the smallest number of researchers that will not be allocated to their chosen team? 15(B) 17(C) 20(D) 25(E) 30 (A) 15(B) 17(C) 20(D) 25(E) 30 (A) 15(B) 17(C

## How to convert a percentage into a fraction or decimal

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### Percentage increase and decrease

Calculations and verification in great detail The first paragraph is an introduction. Percent, p percent ‘out of one hundred’: p percent = p ‘out of one hundred’, p percent is read p ‘percent’, p percent = p/100 = p 100 70 percent = 70/100 = 70 100 = 0.7 percent = 100/100 = 100 100 = 1 percent = 100/100 = 100 100 = 1 percent = 100/100 = 100 100 = 1 percent = 100/100 = 100 100 = 1 percent = 100/100 = 100 100 = What is the percentage of 70 percent of 35? 70 percent of a number equal to 35 equals: 70 percent = 35 percent 70 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent = 35 percent a demonstration
How can we know if the result is correct? If 70 percent of 50 equals 35, then Subtract 35 from 50… And see what we come up with: 70% of the time Notice that multiplying a number by the fraction 100/100,… does not alter its meaning. n/100 = n percent, any number 100/100 = 100 100 = 1 n/100 = n percent, any number

### How to write the percent of a number, 7% of 35

70% * 35 = (70:100)*35 = (70*35):100 = 2450:100 = 24.5We now have: 70 percent of 35 equals 24.5 percent What is the answer to the following question: 70 percent of 35? Steps to a percentage solution: Step 1: The value of our production is 35. Phase 2: We use x to represent the unknown value. Phase 3: Using the formula from step 1, 35=100%. Step 4: x=70 percent is the same. Step 5: This yields a pair of straightforward equations: 35=100%%%%%%%%%%%%%%%%%%%%%%%%%% (1). x=70%%%%%%%%%%%%%%%%%%%%%%%%% (2). Step 6: We get frac35x=frac100%70% by dividing equation 1 by equation 2 and noticing that both the RHS (right hand side) of both equations have the same unit ( percent ). Step 7: The reciprocal of both sides again gives fracx35=frac70100. x = 24.5 in the right arrow As a result, 70 percent of 35 equals 24.5.
35% of the overall *70 = (35:100)*70 = (35*70):100 = 2450:100 = 24.5 *70 = (35*70):100 = 2450:100 = 24.5 Now we have: 35% of 70 equals 24. 5Question: What percentage of 70 is 35 percent? Steps to a percentage solution: Phase 1: The value of our production is 70. Phase 2: We use x to represent the unknown value. Phase 3: Using the formula from step 1, 70=100%. Step 4: x=35 percent is the same. Step 5: This yields a pair of straightforward equations: 70%=100% (1). x=35%%%%%%%%%%%%%%%%%%%%%%%%% (2). Step 6: We have frac70x=frac100% 35 percent by dividing equation 1 by equation 2 and noticing that both the RHS (right hand side) of both equations have the same unit ( percent ). Step 7: The reciprocal of both sides again gives fracx70=frac35100. x = 24.5 in the right arrow As a result, 35 percent of 70 equals 24.5 percent.