nandini11 wrote:
Samantha invests i1 dollars in bond X, which pays r1 percent simple interest annually, and she invests i2 dollars in bond Y, which pays r2 percent simple interest annually. After one year, will she have earned more interest, in dollars, from bond X than from bond Y ?
(1) \((r1)^2 > (r2)^2\)
(2) The ratio of i1 to i2 is larger than the ratio of r1 to r2 .
Why cant 1 be sufficient .
We know that interest cannot be negative , therefore (1) eventually leads to r1> r2 .
The values of i1 and I2 don’t matter , because even when i2 is greater than i1 , the interest would be less .Eg. i1 : 100 r1: 5% , i2: 150 , r2: 3% , i1r1 > i2r2 giving the required result .
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Since we have 4 variables (i1, i2, r1 and r2) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.
Conditions 1) and 2):
Since r1 and r2 are positive, (r1)^2 > (r2)^2 implies r1 > r2 or r1/r2 > 1.
Since i1/i2 > r1/r2 from the condition 2), i1/i2 > r1/r2 > 1 implies i1/i2 > 1 or i1 > i2.
i1 * r1 > i2 * r2.
Thus the interest from the bond X is more than the interest from the bond Y.
Both conditions together are sufficient.
Therefore, C is the answer.
In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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