Hi sud21,
This DS question requires a bit of 'brute force' arithmetic, but the 'math' itself is not that difficult. We're asked for the value of X.
1) The sum of all the unique factors of X is 24
IF...
X = 14, the factors are 1,14,2,7
The sum of the factors is 24 and the answer to the question is 24.
IF...
X = 15, the factors are 1,15,3,5
The sum of the factors is 24 and the answer to the question is 24.
Fact 1 is INSUFFICIENT
2) 10 < X < 20
X can be any integer from 11 to 19, inclusive, but we don't know the exact value of X.
Fact 2 is INSUFFICIENT
Combined, from our prior work, we can already see that there are are least 2 different answers.
Combined, INSUFFICIENT
Final Answer: E
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Rich
Number properties
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.
What is the value of integer x?
(1) The sum of all the unique factors of x is 24.
(2) 10 < x < 20
In the original condition there is 1 variable (x) and thus we need 1 equation to match the number of variable and equation. Since there is 1 each in 1) and 2), D has high probability of being the answer.
In case of 1), x=14(1+2+7+14=24), x=15(1+3+5+15=24)... the answer is not unique, and therefore the condition is not sufficient.
In case of 2), the answer is not unique and therefore the condition is not sufficient.
Using both 1) & 2) together, x=14(1+2+7+14=24), x=15(1+3+5+15=24)....the answer is not unique and therefore the conditions are not sufficient. Therefore the answer is E.
Normally for cases where we need 1 more equation, such as original conditions with 1 variable, or 2 variables and 1 equation, or 3 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.
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Remember equal number of variables and independent equations ensures a solution.
What is the value of integer x?
(1) The sum of all the unique factors of x is 24.
(2) 10 < x < 20
In the original condition there is 1 variable (x) and thus we need 1 equation to match the number of variable and equation. Since there is 1 each in 1) and 2), D has high probability of being the answer.
In case of 1), x=14(1+2+7+14=24), x=15(1+3+5+15=24)... the answer is not unique, and therefore the condition is not sufficient.
In case of 2), the answer is not unique and therefore the condition is not sufficient.
Using both 1) & 2) together, x=14(1+2+7+14=24), x=15(1+3+5+15=24)....the answer is not unique and therefore the conditions are not sufficient. Therefore the answer is E.
Normally for cases where we need 1 more equation, such as original conditions with 1 variable, or 2 variables and 1 equation, or 3 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.
Math Revolution : Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World's First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Unlimited Access to over 120 free video lessons - try it yourself (https://www.mathrevolution.com/gmat/lesson)
See our Youtube demo (https://www.youtube.com/watch?v=R_Fki3_2vO8)
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S1:: Easiest if we try numbers. We should cheat and look ahead at S2 here: if we can find two numbers in that range that work, the answer will be E. If it isn't, the answer should be C. x could be 14 or 15; NOT SUFFICIENT. (Remember to think outside of 10 < x < 20 as well, for instance x = 23 is another solution.)
S2:: Obviously not sufficient.
Since we already anticipated S2 with our numbers in S1, we now know the answer is E and don't have to bother testing any more numbers.
S2:: Obviously not sufficient.
Since we already anticipated S2 with our numbers in S1, we now know the answer is E and don't have to bother testing any more numbers.
