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01 Sep 2011, 05:50
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I found this technique on Manhattan Series. I would like share my learning with you.
Sometimes, fraction problems on the GMAT include unspecified numerical amounts;
often these unspecified amounts are described by variables. In these cases, pick real numbers
to stand in for the variables. To make the computation easier, choose Smart Numbers equal
to common multiples of the denominators of the fractions in the problem.
Example
Lisa spends 3/8 of her monthly paycheck on rent and 5/12 on food. Her roommate, Carrie, who earns twice as much as Lisa, spends 1/4 of her monthly paycheck on rent and 1/2 on food. If the two women decide to donate the remainder of their money to charity each month, what fraction of their combined monthly income will they
donate?
Use Smart Numbers to solve this problem. Since the denominators in the problem are 8, 12, 4 & 2, assign Lisa a monthly paycheck of $24. Assign her roommate, who earns twice as much, a monthly paycheck of $48. The two women's monthly expenses break down as follows:
Rent Food Leftover
Lisa 3/8 of 24 + 5/12 of 24 = 9+10 Leftover = 24-19 = 5
Carrie monthly paycheck = 48
Carrie 1/4 of 48 = 12, 1/2 of 48 = 24---Leftover= 48 - (12 + 24) = 12
The women will donate a total of $17, out of their combined monthly income of $72.
17/72 is the Answer.
Sometimes, fraction problems on the GMAT include unspecified numerical amounts;
often these unspecified amounts are described by variables. In these cases, pick real numbers
to stand in for the variables. To make the computation easier, choose Smart Numbers equal
to common multiples of the denominators of the fractions in the problem.
Example
Lisa spends 3/8 of her monthly paycheck on rent and 5/12 on food. Her roommate, Carrie, who earns twice as much as Lisa, spends 1/4 of her monthly paycheck on rent and 1/2 on food. If the two women decide to donate the remainder of their money to charity each month, what fraction of their combined monthly income will they
donate?
Use Smart Numbers to solve this problem. Since the denominators in the problem are 8, 12, 4 & 2, assign Lisa a monthly paycheck of $24. Assign her roommate, who earns twice as much, a monthly paycheck of $48. The two women's monthly expenses break down as follows:
Rent Food Leftover
Lisa 3/8 of 24 + 5/12 of 24 = 9+10 Leftover = 24-19 = 5
Carrie monthly paycheck = 48
Carrie 1/4 of 48 = 12, 1/2 of 48 = 24---Leftover= 48 - (12 + 24) = 12
The women will donate a total of $17, out of their combined monthly income of $72.
17/72 is the Answer.
21 May 2014, 00:19
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This is a great time-saving technique.
Here's another question to practice this technique:
Sarah and Joe are a couple. Sarah puts 1/9 of her monthly savings in Fixed Deposits, 5/12 in Mutual Funds and the rest in their joint savings account. Joe, who saves 40% more than Sarah, puts 1/8 of his savings in a Fixed Deposit, 5/6 in Mutual Funds and the rest in the savings account. What fraction of their combined savings lies in the joint savings account?
In the post above, Carrie's salary was a whole number multiple of Lisa's salary. (Carrie's salary = 2*Lisa's salary). In the current question however, Joe's savings are a fractional multiple of Sarah's savings:
Let Joe's savings be J
Sarah's savings be S
J = (1+40/100)*S = (1+2/5)*S = 7/5*S
So, when we apply the smart number technique, we should also consider the fraction 7/5 while choosing our number.
How do we choose a smart number for Sarah's savings?
The fractions in play here are: 1/9, 5/12, 7/5, 1/8, 5/6
So, we will choose the Least Common Multiple of 9, 12, 5, 8,6.
That number will be 360.
So, S= 360
So, Sarah's Fixed Deposit, SF= 360/9 = 40
Sarah's Mutual Funds, SM= (5/12)*360 = 150
Sarah's Saving Account Deposits, SS= 360 - (40+150) = 170
J = (7/5)*360 = 504
Joe's Fixed Deposit, JF= 504/8 = 63
Joe's Mutual Funds, JM = (5/6)*504 = 5*84 = 420
Joe's Saving Account Deposits, JS = 504 - (63+420) = 21
So, Total Fraction in Savings Account for the couple = (SS+JS)/(S+J) = (170+21)/(360+504) = 191/864
Here's another question to practice this technique:
Sarah and Joe are a couple. Sarah puts 1/9 of her monthly savings in Fixed Deposits, 5/12 in Mutual Funds and the rest in their joint savings account. Joe, who saves 40% more than Sarah, puts 1/8 of his savings in a Fixed Deposit, 5/6 in Mutual Funds and the rest in the savings account. What fraction of their combined savings lies in the joint savings account?
SOLUTION
In the post above, Carrie's salary was a whole number multiple of Lisa's salary. (Carrie's salary = 2*Lisa's salary). In the current question however, Joe's savings are a fractional multiple of Sarah's savings:
Let Joe's savings be J
Sarah's savings be S
J = (1+40/100)*S = (1+2/5)*S = 7/5*S
So, when we apply the smart number technique, we should also consider the fraction 7/5 while choosing our number.
How do we choose a smart number for Sarah's savings?
The fractions in play here are: 1/9, 5/12, 7/5, 1/8, 5/6
So, we will choose the Least Common Multiple of 9, 12, 5, 8,6.
That number will be 360.
So, S= 360
So, Sarah's Fixed Deposit, SF= 360/9 = 40
Sarah's Mutual Funds, SM= (5/12)*360 = 150
Sarah's Saving Account Deposits, SS= 360 - (40+150) = 170
J = (7/5)*360 = 504
Joe's Fixed Deposit, JF= 504/8 = 63
Joe's Mutual Funds, JM = (5/6)*504 = 5*84 = 420
Joe's Saving Account Deposits, JS = 504 - (63+420) = 21
So, Total Fraction in Savings Account for the couple = (SS+JS)/(S+J) = (170+21)/(360+504) = 191/864
22 May 2014, 06:53
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Caution while using Smart Number !
Apologize for playing the devil's advocate
Never use Smart number if question involves values (not ratio or %ages) or Final question to be answered requires a value. Example, if we need to find out the total donation (anyways more info. would be provided to answer this).
Apologize for playing the devil's advocate
Never use Smart number if question involves values (not ratio or %ages) or Final question to be answered requires a value. Example, if we need to find out the total donation (anyways more info. would be provided to answer this).
