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by gdk800 » Sun Nov 28, 2010 9:57 pm
1) If n denotes a number to the left of 0 on the number line such that square of n is less than 1/100. Then reciprocal of n must be
a. Less than -10.
b. Between -1 and -1/10.
c. Between -1/10 and 0.
d. Between 0 and 1/10.
e. Greater than 10.

OA is A

2) A car averages 25 miles/gallon when driven in city and 40 miles/gallon when driven on highway. According to these rates, which of following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
a. 28
b. 30
c. 33
d. 36
e. 38

OA is D

3) Attached is an image. On the number line, its visible that according to Option B (z>y) is true but its not the OA.

OA is E

Image
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Source: — Problem Solving |

by Rahul@gurome » Sun Nov 28, 2010 10:07 pm
Question Number 1:
gdk800 wrote:1) If n denotes a number to the left of 0 on the number line such that square of n is less than 1/100. Then reciprocal of n must be
a. Less than -10.
b. Between -1 and -1/10.
c. Between -1/10 and 0.
d. Between 0 and 1/10.
e. Greater than 10.

OA is A
As, n² < 1/100
=> -1/10 < n < 1/10
=> n > -1/10 ........... As n < 0
=> 1/n < -10 ........... Change of inequality sign as n < 0

The correct answer is A.
Rahul Lakhani
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by Rahul@gurome » Sun Nov 28, 2010 10:15 pm
Question Number 2:
gdk800 wrote:2) A car averages 25 miles/gallon when driven in city and 40 miles/gallon when driven on highway. According to these rates, which of following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
a. 28
b. 30
c. 33
d. 36
e. 38

OA is D
Miles driven in city = 10 => Fuel consumed = 10/25 gallons
Miles driven on highway = 50 => Fuel consumed = 50/40 gallons

Total fuel consumed = (10/25 + 50/40) gallons = (80 + 250)/200 gallons = 33/20 gallons
Total distance traveled = (10 + 50) miles = 60 miles

Average miles per gallons = 60/(33/20) = (60*20)/33 = (20*20)/11 ≈ 36

The correct answer is D.
Rahul Lakhani
Quant Expert
Gurome, Inc.
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
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by Rahul@gurome » Sun Nov 28, 2010 10:29 pm
gdk800 wrote:3) Attached is an image. On the number line, its visible that according to Option B (z>y) is true but its not the OA.

OA is E
No, it's not! :)
Option B says xz > xy!
Now as x < 0, canceling x on both sides will reverse the inequality sign! (Think about it!) Thus, z < y, which is not true.

To solve the problem analyze the options one by one.
  • (1) x + y > y => As x and y both negative (x + y) certainly less than both x and y. INCORRECT
    (2) xz > xy => Explained earlier! (Another explanation : x and y negative but z positive => xz always negative and xy always positive => xy > xz) INCORRECT
    (3) tz < z => As z is positive this implies t < 1. INCORRECT
    (4) m^u < 0 => m = -1, u = 2 => m^u = 1. INCORRECT
    (5) t^m > 0 => t is positive and m = -1 => t^m = t^(-1) = 1/t > 0. CORRECT
The correct answer is E.
Rahul Lakhani
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Gurome, Inc.
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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+91-99201 32411 (India)
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by gdk800 » Sun Nov 28, 2010 11:42 pm
Thanks Rahul, yes i realized about the 3rd question as soon as you wrote x is less than 0.
But could you please elaborate on the 1st question a bit more.

As n > -1/10
=>10 > -1/n
Multiplying both sides by -1 and thus the inequality reverses sign
=>-10 < 1/n

Thus 1/n should be greater and not less than -10.....

Plz explain!!!
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by Rahul@gurome » Sun Nov 28, 2010 11:58 pm
gdk800 wrote:Thanks Rahul, yes i realized about the 3rd question as soon as you wrote x is less than 0.
But could you please elaborate on the 1st question a bit more.

As n > -1/10
=>10 > -1/n [As n is negative, cross multiplication will also revert the inequality sign! Thus it will be 10 < -1/n]
Multiplying both sides by -1 and thus the inequality reverses sign
=>-10 < 1/n

Thus 1/n should be greater and not less than -10.....

Plz explain!!!
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Join the discussion