how many 3 digit nos. are dere whose digits sums up to 16?
@imrover said:@mohitjainthis way we are only considering the last three digits. the complete number is 523_ _ _. How can we conclude just by looking at the last three digits?
523xyz is divisible by 504, where xyz is three digit number
=> 523000 + xyz is divisible by 504
=> 504000 + 19000 + xyz is divisible by 504
=> 352 + xyz is divisible by 504
So, 352 + xyz = 504 or 1008
=> xyz = 152 or 656
Two possible numbers
@jain4444 said:Consider all three-digit numbers that are greater than the sum of the squares of their digits by exactly 543. What are the last three digits of the sum of these numbers?
a(100-a)+b(10-b)+c(1-c)=543
Since max (b(10-b))=25 and max(c(1-c)) = 0 => Min (a(100-a)) = 518 => Min (a)=6
Since min (b(10-b))=0 and min(c(1-c)) = -72 => Max (a(100-a)) = 615 => Max (a)=6
Hence, a=6. So the original equation reduces to c(c-1) - b(10-b)=21
Since c(c-1) is even, b must be odd and will have a conjugate pair wrt 10.
Possibilities include-> for b=(3,7), c = 7, and for b=(1,9), c = 6
So, the sum of numbers = 637+677+616+696=2626. So, last three digits are 626
Team BV - Vineet
@mohitjain said:how many 3 digit nos. are dere whose digits sums up to 16?
If the number is abc, then for values of a from 1 through 7, the possibilities are Summation (4 to 10)
For a = 8 and 9, possibilities are 9 and 8 respectively.
So total such numbers = 66
Team BV - Vineet
@mohitjain said:how many 3 digit nos. are dere whose digits sums up to 16?
abc is the number, then
a + b + c = 16
C(18, 2) = 153 ways
When one of a, b, c is 10 or more then
a' + b + c = 6
C(8, 2) = 28 ways
153 - 3*28 = 69 numbers
When a is 0, three possibilities 097, 088, 079
So, 66 such numbers
for 6 rolls of film he got one roll film free. for camera he gets 3 rolls means.. one cam is equal to 18 rolls of film
Hi Please Help !
Q The average of 8 persons in a comitee is increased by 2 years, when two men aged 35 and 45 years area substituted by two women. Find the average age of two women ??
Please Tell the Approach !??
@ananyboss said:Hi Please Help ! Q The average of 8 persons in a comitee is increased by 2 years, when two men aged 35 and 45 years area substituted by two women. Find the average age of two women ??Please Tell the Approach !??
The women add (8*2) years to the group. That means 80 years goes out and 96 comes in. Average age=96/2= 48? :/
@vbhvgupta said:A shopkeeper bought an article for 360. the profit made by the shopkeeper after selling it after a 11.11% discount is 40. FIND marked price
i would like to add a simpler approach for this question..
given: CP = 360
discount is 11.11% = 1/9%
Let MP be "x" so after the discount x-x/9=8x/9 is the price. Now 40rs is the profit on this
So 8x/9-40=360
x=450
given: CP = 360
discount is 11.11% = 1/9%
Let MP be "x" so after the discount x-x/9=8x/9 is the price. Now 40rs is the profit on this
So 8x/9-40=360
x=450
@Angadbir said:All no.s are of the form 2k+1So,(2a + 1) + (2b + 1) + (2c + 1) + (2d + 1) + (2e + 1) = 192(a + b + c + d + e) = 14a + b + c + d + e = 7 --> C(11,4) = 330 But if we are looking for unordered sets, we would have to eliminate the repeated cases as below:When all 5 of a,b,c,d,e are same = 0 waysWhen 4 are same -> These are repeated 5 times4x + y = 7 -> y=3,7 -> 2 waysWhen 3 are same and other 2 are same => These are repeated 5!/3!2! = 10 times3x + 2y = 7 -> y = 2 -> 1 wayWhen 3 are same and other 2 are distinct => These are repeated 5!/3! = 20 times3x + y + z = 7x = 0 -> 3 waysx = 1 -> 1 waysx = 2 -> 1 way2 same, 2 same, 1 distinct => These are repeated 5!/2!2! = 30 times2x + 2y + z = 7x = 0 -> 3 ways2 same, 3 distinct => These are repeated 60 times2x + y + z + t = 7 x = 0 -> 1 wayx = 1 -> 1 wayTotal unordered sets = 2 + 1 + 5 + 3 + 2 = 13So 13 ways to achieve this.
Sir can you please explain When 4 are same -> These are repeated 5 times
this is because of 5!/4! but then why do we need to calculate the 4x+y=7 ?
Please explain
this is because of 5!/4! but then why do we need to calculate the 4x+y=7 ?
Please explain
@Asfakul said:Sir can you please explain When 4 are same -> These are repeated 5 timesthis is because of 5!/4! but then why do we need to calculate the 4x+y=7 ?Please explain
When 4 are same, then among a, b, c, d, e, four are equal
Since a + b + c + d + e = 7, we can say that
4a + e = 7
@Koushik98 said:Triangle ABC has unit area. P, Q, R divides the three sides in the ratios as shown in figure. Find the shaded area of triangle.
@chillfactor Sir, can you please take a look at this question? There is some uncertainty...
regards
scrabbler
regards
scrabbler
@scrabbler said:@chillfactor Sir, can you please take a look at this question? There is some uncertainty...regardsscrabbler
11/24
Check the attachment
Hi,
I don't want to do this with the mechanical approach using lot of equations etc, can anyone help ?
An average of marks of 13 people is 40. Average of first 7 people is 42, and average of Last seven is 35, Find the Marks of 7th Person ?
Approach !
@ananyboss said:Hi,I don't want to do this with the mechanical approach using lot of equations etc, can anyone help ?An average of marks of 13 people is 40. Average of first 7 people is 42, and average of Last seven is 35, Find the Marks of 7th Person ?Approach !
42*7 + 35*7 - 40*13 = 19
@ananyboss said:Hi,I don't want to do this with the mechanical approach using lot of equations etc, can anyone help ?An average of marks of 13 people is 40. Average of first 7 people is 42, and average of Last seven is 35, Find the Marks of 7th Person ?Approach !
You can see that if we add marks of first 7 and last seven then marks of 7th person will be added twice. So just subtract marks of all from this to get the marks of 7th person
Marks of 7th person = 7*42 + 7*35 - 13*40 = 19
@ananyboss said:Hi,I don't want to do this with the mechanical approach using lot of equations etc, can anyone help ?An average of marks of 13 people is 40. Average of first 7 people is 42, and average of Last seven is 35, Find the Marks of 7th Person ?Approach !
total marks of 13 = 520.......(1)
total marks of 14 guys= 7*42+7*35..........(2)
marks of 7th person = (2)-(1)
actually it will be calculated in just one line
total marks of 14 guys= 7*42+7*35..........(2)
marks of 7th person = (2)-(1)
actually it will be calculated in just one line
@chillfactor said:11/24Check the attachment
Thank you Sir...mera bhi yehi aaya tha, by different method (see attached), but the OA given is different so tension ho gaya 😞
http://www.pagalguy.com/posts/4896330
Solution given is using Mass Point Geometry (which I have no clue of) and I can't understand what has been done there...so I was wondering what I had done wrong. But now am relieved, will trust your word any day :)
regards
scrabbler
http://www.pagalguy.com/posts/4896330
Solution given is using Mass Point Geometry (which I have no clue of) and I can't understand what has been done there...so I was wondering what I had done wrong. But now am relieved, will trust your word any day :)
regards
scrabbler
@ananyboss said:Hi,I don't want to do this with the mechanical approach using lot of equations etc, can anyone help ?An average of marks of 13 people is 40. Average of first 7 people is 42, and average of Last seven is 35, Find the Marks of 7th Person ?Approach !
sum of all = 13x40 = 520
sum of 1st 7 + sum of last 7 = 539 = sum of all + (the 7th person)
=> 7th person = 539 - 520 = 19