Official Quant thread for CAT 2013

MBA CAT 2024
14143
@TootaHuaDil said:
Find the smallest number which when divided by 7,8 and 9 leaves a remainder of 5, 4 and 2. Please solve with explanation.
Direct application of Chinese remainder theorem
7x+5=8y+4=9z+2
7x+5=8y+4
x=(8y-1)/7=y-1)/7

y=7k+1
8(7k+1)+4=9z+2
56k+12=9z+2
z=56k+10 / 9 = (2k+1 )/9
k=9m+4
so number is 56k+12 =56(9m+4)+12=224+12=236 ???
14144
@techsurge almost there. It's 234
14145
@TootaHuaDil said:
@techsurge almost there. It's 234
not possible 234 is divisble by 9 as its digit sum is 9
14146
@techsurge said:
not possible 234 is divisble by 9 as its digit sum is 9
Ohh...yeah sorry..book has printing mistake in last line. It's 236 (Y)
14147
@gupanki2 said:
A student was given 8 two-digit numbers to add, by a teacher. If the student reversed each number and added the results, the sum of the numbers would be 36 more than the actual sum. Find the excess of the sum of the units digits over that of the tens digits.
4???

take 7 11's and 15
14148
@sails Nahi dostttttttttttttttttttttttttttttt................... ๐Ÿ˜ž though appreciate ya efforts here... answer is 25604
14149
@gupanki2 said:
Ashok went on a tour. He visited a total of 8 cities. In each city he spent เคฐ2 less than half the amount he had with him. He spent เคฐ100 in the last city he visited. Find the amount he had initially (in เคฐ).
@naga25french Sir, pls help
Can this question be solved by application of fibonnaci series
14150
@sails u r correct for city 8th but seems u made some slight logical mistake frm 7th city to 1st city... in 7th city ... 404(inital amt) -200 (spent) = 204 (left after city 7= inital amt for city 8)... go on till 1st u will get the answer... let me knw fr should u have any doubts.... meine bada sirr mara hai isme :P

**deleted previous comment... which was same as this comment... posted twice beacuse got failure error on posting previous post
14151
@gupanki2 said:
@sails Nahi dostttttttttttttttttttttttttttttt................... though appreciate ya efforts here... answer is 25604

ya got the mistake..i was taking the half of amount spent instead of taking half of remaining amout...so only got wrong...
Actually there is an easier way which i got now..if you do takin initially amount he had as x..and go on you will fond a pattern that
Amount spent on a city is x-4/2^n ....so directly accordin to question
x-4/2^8 =100
so x=25604..:D Cheerss...:D
14152
@sails yessssssss...... its good to commit mistake and to learn from those ๐Ÿ˜ƒ cheers
14153
@gupanki2 said:
@sails yessssssss...... its good to commit mistake and to learn from those cheers
any more questions for 2day..??..:)
14154
@sails bass bhaiiii..... subah (12 pm) office bhi jana hai .... ๐Ÿ˜ž kal will post... :)
14155
The ratio of the present ages of a man and his wife is 5 : 4. After 20 years, the ratio of the ages of the man and his wife could be
14156
@gupanki2 the answer to your question - http://www.algebra.com/algebra/homework/word/age/Age_Word_Problems.faq.question.570812.html
14157
M is a two digit number which has the property that: the product of factorial of its digit>sum of factorial of its digits.how many values of M exists?
A)56 B)64 C)63 D)none of these
14158
@shattereddream from 10 to 99 we have 90 2 digits number.We will subtract those numbers that don't follow the rule

10,20.....90 9 numbers
11,21,31.....91 9 numbers
12,13......19 8 numbers

so total 26

90-26= 64 numbers.
14159
@shattereddream said:
M is a two digit number which has the property that: the product of factorial of its digit>sum of factorial of its digits.how many values of M exists? A)56 B)64 C)63 D)none of these
Is it D?
14160
@nole said:
@shattereddream from 10 to 99 we have 90 2 digits number.We will subtract those numbers that don't follow the rule10,20.....90 9 numbers11,21,31.....91 9 numbers12,13......19 8 numbersso total 2690-26= 64 numbers.
Actually i have done it with some other method , yours is also a nice method . thanks
14161
@shattereddream said:
M is a two digit number which has the property that: the product of factorial of its digit>sum of factorial of its digits.how many values of M exists? A)56 B)64 C)63 D)none of these
Is it D?
14162

Yes D it is the answer is 64