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arithmetic problem

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by topspin360 » Mon Dec 24, 2012 1:49 pm
can anyone suggest the most efficient way of doing this problem? OR, more importantly, GMAT arithmetic in general.. any resources I can use to get better at it?

Which of the following expressions has the greatest value?

A) 0.456
B) 1/2 − (1/2)^4
C) 300/650
D) 3*(3/19)
E) sqrt(0.17)

Please let me know if anyone knows additional general techniques for gmat arithmetic. Books don't seem to have any useful tactics.
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by puneetkhurana2000 » Mon Dec 24, 2012 8:35 pm
LCM will be tedious I believe so approximation can work.

A) 0.456
B) 1/2 - (1/2)^4 = 7/16 = 7 * 6% = .42(approx)
C) 300/650 = 6/13 = 6 * 7% = .42(approx)
D) 3*(3/19) = 9/19 = 9 * 5% = .45(approx)
E) sqrt(0.17) -- closer to 0.4

So, now its down to A or D. From here its better to actually calculate the expression 9/19 to three decimal places and it is 0.473.

Answer D.
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by puneetkhurana2000 » Mon Dec 24, 2012 9:05 pm
Alternately we can solve this by:-

A) 0.456
B) 1/2 - (1/2)^4 = 7/16 = 40% of 16(6.4) + less than 5% of 16(0.8) = < 0.45(approx)
C) 300/650 = 6/13 = 40% of 13(5.2) + little more than 6% of 13(0.78) = > 0.46(approx)
D) 3*(3/19) = 9/19 = 40% of 19(7.6) + little more than 7% of 19(1.33) = > 0.47(approx)
E) sqrt(0.17) -- closer to 0.4

Answer D.
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by tabsang » Tue Dec 25, 2012 3:32 am
Thanks Puneet for the solutions but I'm still a bit confused :(
This type (approximation) has been a weakness.
I did get [spoiler](D)[/spoiler] but I'm not sure if it was the right approach :(

Experts please help :( :(
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by buzzdeepak » Fri Jan 04, 2013 3:19 pm
1. 0.456 (leave it as it is)

2. 1/2 - 1/2^4 = 1/2 (1-1/8) = 1/2*7/8 = 1/2 * 0.875 = 0.43... (We know 7/8 = 0.875) and since 2nd decimal is 3, no need to calculate the 3rd decimal. At most it would be 0.44 if the 3rd decimal is >5

3. 300 / 650 = 6/13 (leave it as it is for now)

4. 9 / 19
Now, since I am not sure between 6/13 and 9/19 which one is greater, cross multiply
6*19 = 114
9*13 = 117
=> 9/19 is greater between the 2, keep it (so till now, we have eliminated 2 and 3, leave 9/19 as it is for now)

5. sqrt (0.17) = very close to 0.4 (something like 0.41 or 0.43 at the most, so eliminate)

Now, all we are left with are 1 and 4. Since the numbers are too close, I found 9/19 to be 0.47... (no need to calculate the 3rd decimal now since 7 > 6, if we round answers 1 and 3)

Thus, D is the answer.

Note: Need to be comfortable with ratios 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8 and 1/9 and their multiples so we can quickly switch between ratios and decimals

Hope this helps.
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by Aanderson » Fri Jan 04, 2013 7:27 pm
I agree with solution above, dont think there is any easier way to do this, just have to use approximation.
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by GMATGuruNY » Fri Jan 04, 2013 8:22 pm
topspin360 wrote:can anyone suggest the most efficient way of doing this problem? OR, more importantly, GMAT arithmetic in general.. any resources I can use to get better at it?

Which of the following expressions has the greatest value?

A) 0.456
B) 1/2 − (1/2)^4
C) 300/650
D) 3*(3/19)
E) sqrt(0.17)
One way to compare A, B, C and D is suggested by answer choice B: calculate the difference between each answer choice and 1/2.

A: .5 - .456 = .044 = 44/1000 = 11/250 ≈ 1/22.

B: 1/2 - (1/2 − (1/2)�) = 1/2 - 1/2 + 1/16 = 1/16.

C: 1/2 - 300/650 = 325/650 - 300/650 = 25/650 = 1/26.

D: 1/2 - 3(3/19) = 1/2 - 9/19 = 19/38 - 18/38 = 1/38.

Since D yields the smallest difference, D is the CLOSEST TO 1/2.
Eliminate A, B and C.

To compare D and E, SQUARE them and put them over a COMMON DENOMINATOR:

D: (9/19)² = 81/361 ≈ 81/360 = 9/40 = 45/200.

E: (√.17)² = 17/100 = 34/200.

Since 45/200 > 34/200, eliminate E.

The correct answer is D.
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by manihar.sidharth » Mon Mar 17, 2014 8:13 pm
What is the concept behind this :
"
Now, since I am not sure between 6/13 and 9/19 which one is greater, cross multiply
6*19 = 114
9*13 = 117
=> 9/19 is greater between the 2, keep it (so till now, we have eliminated 2 and 3, leave 9/19 as it is for now) "
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by Matt@VeritasPrep » Mon Mar 17, 2014 11:48 pm
Another safe way is to perform a series of comparisons, starting with the easiest two values. Before we do so, however, let's simplify each answer:

A) 456/1000 = 57/125 (divide both the top and the bottom by 8)
B) 1/2 - 1/16 = 7/16
C) 300/650 = 6/13 (divide both the top and the bottom by 50)
D) 9/19
E) √(17/100) = √17/10

A and C seem relatively easy to compare. To compare these, we can follow a simple process. Assume 6/13 > 9/19, then cross-multiply. If the inequality you get is true, then 6/13 was bigger than 9/19. If the inequality you get is false, then it wasn't.

6/13 > 9/19 implies 6*19 > 9*13 or 114 > 117. Whoops! So 9/19 > 6/13. Eliminate C.

Now compare D to A. Assume 9/19 > 57/125. This implies 9*125 > 19*57, or 3*125 > 19*19, or 375 > 361. This is true, so D is still the biggest.

Now compare D to B. 9/19 > 7/16 implies 9*16 > 7*19 implies 144 > 133, which is true. So D is still the biggest.

Last we have D vs E. 9/19 > √17/10 implies 9*10 > 19*√17 or 90 > appx 19*4.25, which is true, so D is the biggest.

This problem is going to take time no matter how you approach it: the answer choices aren't very well designed and don't reward your ingenuity. On the GMAT, there would likely be one difficult insight that made the greatest value immediately clear rather than a series of unwieldy numbers designed to measure how quickly and accurately you can do arithmetic. (Perhaps something that seems scary at first but yields to a surprisingly simple approach, such as "Which of these is bigger, 2^√3 or 3^√2?")
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