Quantitative Questions For CAT
December 16th, 2009 Posted in Quantitative Ability
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1. When a certain two-digit number is added to another two digit number having the same digits in reverse order, the sum is a perfect square. How many such two-digit numbers are there?
a. 4
b. 6
c. 8
d. 10
2. Anuj likes to jog in a park. While jogging he also calculates his speed and the number of steps taken by him. He observes that the steps taken by him per minute are 5 times his speed in km/hr. What is the distance he covers per step if he jogs at a uniform speed?
a. 5/3m
b. 10/3m
c. 100/3m
d. Data insufficient
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December 17th, 2009 at 2:26 am
1.c
10x+y+10Y+x = 11(x+y) is a perfect square..The solutions could be (2,9),(3,8),(4,7),(5,6),(6,5),(7,4),(8,3),(9,2)
2.b
if the speed be xkm/hr then he takes 5x steps per minute.
He takes x/60 km /minute..
so 5x steps === (x/60)*1000 m
1 step === 10/3 m
December 17th, 2009 at 2:39 am
1. C
2. B
explanation by govind is absolutely correct.
Even I did in same way.
December 17th, 2009 at 3:09 am
C n B
Even I did the same way!
December 17th, 2009 at 10:24 am
c
b
December 17th, 2009 at 11:19 pm
1. c
1. c
Let the two digit number be ab.
Value of ab = 10a + b
We have
10a + b + 10b + a = 11(a + b) is a perfect square.
Since 11(a + b) is a perfect square.
Therefore (a + b) should also be a multiple of 11 but a + b cannot be equal to 22 or more as a and b cannot be more than 9.
Therefore, a + b = 11
Now we have these 8 solutions.
(2, 90, (3, 8), ., (9, 2)
2. b
Let n = number of
Steps taken by anuj per minute.
Therefore his speed will be n/5km/hr.
Again, let us assume
X = Distance in meters he covers in each step.
Therefore distance covered by Anuj in meters per min = n × x
Therefore, distance covered by him per hour in km will be
= n × x × 60/1000
Therefore n × x × 60/1000 = n.5
X = 10/3 meters.
February 7th, 2010 at 9:29 am
yeah!!!!!!1
1. c
2. b
did the very same way as is mentioned above……..