OG 55 Why I can't use a smart number here?

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lotrgandalf: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Sat May 30, 2015 9:36 am

by lotrgandalf » Sat Jul 23, 2016 7:55 am

Smart numbers can be picked if no amounts are given in the problem; when any amount or total is given don't pick smart numbers.
What am I doing wrong by choosing a smart number for gross and deduction
I solved OG 13, DS Q55 in the following way

Guy's net income equals his gross income minus his deductions. By what percent did Guy's net income change on January 1, 1989, when both his gross income and his deductions increased?

(1) Guy's gross income increased by 4 percent on January 1, 1989.
(2) Guy's deductions increased by 15 percent on January 1, 1989.

Solution: Choose smart number for Gross(200) and Deduction(100).

old change new
--------------------------------------------
Net |300 | x |323
Gross |200 | 8 |208
Deduction |100 | 15 |115

therefore, x = 323-300/300. Hence (C).
But the correct answer is (E). I can solve this problem by forming algebraic equations, but why I can't use a smart number here?

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Source: Beat The GMAT — Data Sufficiency | Sat Jul 23, 2016 7:55 am

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by [email protected] » Sat Jul 23, 2016 9:19 am

Hi lotrgandalf,

You can absolutely TEST VALUES on this question, but you have to do enough work to prove whether the answer to the question stays the same or changes.

You seem comfortable with the idea that each of the two Facts is insufficient on its own, so I'll jump straight to combining the Facts:

(1) Guy's gross income increased by 4 percent on January 1, 1989.
(2) Guy's deductions increased by 15 percent on January 1, 1989.

IF....
Old gross income = 200
New gross income = 208
Old deductions = 100
New deductions = 115

Old net income = 200 - 100 = 100
New net income = 208 - 115 = 93
Percent change = (93 - 100)/100 = -7/100 = 7% decrease

But what happens if we TEST a different VALUE for the old income....?

IF....
Old income = 300
New income = 312
Old deductions = 100
New deductions = 115

Old net income = 300 - 100 = 200
New net income = 312 - 115 = 197
Percent change = (197 - 200)/200 = -3/200 = 1.5% decrease

The answer to the question has now changed. Thus, we have an inconsistent result and an insufficiency.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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lotrgandalf: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Sat May 30, 2015 9:36 am

by lotrgandalf » Sat Jul 23, 2016 10:06 am

[email protected] wrote:Hi lotrgandalf,

You can absolutely TEST VALUES on this question, but you have to do enough work to prove whether the answer to the question stays the same or changes.

You seem comfortable with the idea that each of the two Facts is insufficient on its own, so I'll jump straight to combining the Facts:

(1) Guy's gross income increased by 4 percent on January 1, 1989.
(2) Guy's deductions increased by 15 percent on January 1, 1989.

IF....
Old gross income = 200
New gross income = 208
Old deductions = 100
New deductions = 115

Old net income = 200 - 100 = 100
New net income = 208 - 115 = 93
Percent change = (93 - 100)/100 = -7/100 = 7% decrease

But what happens if we TEST a different VALUE for the old income....?

IF....
Old income = 300
New income = 312
Old deductions = 100
New deductions = 115

Old net income = 300 - 100 = 200
New net income = 312 - 115 = 197
Percent change = (197 - 200)/200 = -3/200 = 1.5% decrease

The answer to the question has now changed. Thus, we have an inconsistent result and an insufficiency.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

When absolute or concrete numbers are not asked, how can I decide whether choosing SMART NUMBER is better or forming algebraic equations?
Smart Numbers are powerful tool in case absolute amounts are not asked.

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GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Jul 23, 2016 6:04 pm

Hi lotrgandalf,

With enough practice, you're going to find that most of the Quant questions that you'll see on Test Day can be solved by TESTing VALUES, so the decision to use this approach is probably easier than you think it is. I use it so often that I generally go into Quant questions assuming that I'll use that approach, then pivot to a different approach if the information/clues in the prompt tell me to.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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