By how much is three fifths of 350 greater than four sevenths of 210? Compute the exact numerical difference between these two quantities.

Introduction / Context:
This question tests your ability to work with fractions applied to whole numbers and to compare two resulting values. It looks very simple, but such questions are common in speed tests where quick and accurate calculation is required. The key is to compute three fifths of 350 and four sevenths of 210 separately and then subtract to find how much one quantity is greater than the other.

Given Data / Assumptions:

• We need to find 3/5 of 350.
• We also need to find 4/7 of 210.
• We must compute how much the first quantity is greater than the second.
• All numbers are real and standard arithmetic rules apply.

Concept / Approach:
The concept here is straightforward fractional multiplication. To find a fraction of a number, multiply the number by the numerator and divide by the denominator. After obtaining both values, we compare them by subtraction. Because both numbers are multiples of the denominators, the calculations are especially easy, which is typical for exam style questions designed to be done mentally or with very little working.

Step-by-Step Solution:
Compute three fifths of 350: (3/5) * 350. First, 350 / 5 = 70. Then, 3 * 70 = 210. So, three fifths of 350 is 210. Now compute four sevenths of 210: (4/7) * 210. First, 210 / 7 = 30. Then, 4 * 30 = 120. So, four sevenths of 210 is 120. Now find how much the first is greater than the second. Difference = 210 - 120 = 90.

Verification / Alternative check:
We can verify by checking that the fraction calculations are correct. Since 3/5 means 60 percent, 60 percent of 350 is indeed 210, because 10 percent is 35 and 6 * 35 = 210. For 4/7 of 210, note that 1/7 of 210 is 30, so 4/7 is 4 * 30 = 120. The difference 210 - 120 is clearly 90. The computations are consistent using both the fraction method and the percentage interpretation, which confirms the result.

Why Other Options Are Wrong:
100 and 110: These would result from miscalculating one of the fractions or from incorrect subtraction such as 220 minus 120 or 210 minus 100.
120: This would suggest confusing the result of four sevenths of 210 with the difference value itself.
80: This comes from a mistaken subtraction such as 200 minus 120. Careful arithmetic eliminates these incorrect options.

Common Pitfalls:
A common mistake is to miscompute the fraction by multiplying directly without simplifying first, which may cause errors. For example, some students might try 3 * 350 / 5 in one step and miscalculate. Another pitfall is to subtract in the wrong order and answer how much the smaller is less than the larger without reading the question carefully. Always compute each fraction step by step and then subtract larger minus smaller as requested.

Final Answer:
Three fifths of 350 is greater than four sevenths of 210 by 90.