Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 61)
61.
When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?
Answer: Option
Explanation:
x = 13p + 11 and x = 17q + 9
13p + 11 = 17q + 9
17q - 13p = 2
| q = |
2 + 13p |
| 17 |
| The least value of p for which q = | 2 + 13p | is a whole number is p = 26 |
| 17 |
x = (13 x 26 + 11)
= (338 + 11)
= 349
Discussion:
47 comments Page 1 of 5.
Sudhanshu said:
5 years ago
Here is a simpler way for all of you.
Let no. be N, then;
N = 13a+11. > N-11 =13a (eq. 1).
N = 17b+9. > N-9 =17b (eq. 2).
Thus eq 1 and 2 suggest that N-11 should be divisible by 13 and N-9 should be divisible by 17.
N=349 satisfies both conditions!
Let no. be N, then;
N = 13a+11. > N-11 =13a (eq. 1).
N = 17b+9. > N-9 =17b (eq. 2).
Thus eq 1 and 2 suggest that N-11 should be divisible by 13 and N-9 should be divisible by 17.
N=349 satisfies both conditions!
(14)
Kasala ravichandra said:
2 years ago
if x = 13a - 11.
13a = x-11.
a = x-11/13
The ans a)339 sub in x place.
a = 339-11/13 = 25.2=> Not divisible by 13.
...take ans b)349 sub x place
a=349-11/13=26
So, 349 is completely divisible by 13 then the option B is the correct answer.
13a = x-11.
a = x-11/13
The ans a)339 sub in x place.
a = 339-11/13 = 25.2=> Not divisible by 13.
...take ans b)349 sub x place
a=349-11/13=26
So, 349 is completely divisible by 13 then the option B is the correct answer.
(8)
Souriddha Sen said:
1 year ago
@All.
According to me, "The least value of p for which. " ---the question didn't ask for the least value that satisfies the conditions. The question implies a unique number: "What is THE number?", not "What might be one such number/what is the smallest such number?".
Since the conditions given does not have a unique solution, "Data inadequate" should be the correct answer.
According to me, "The least value of p for which. " ---the question didn't ask for the least value that satisfies the conditions. The question implies a unique number: "What is THE number?", not "What might be one such number/what is the smallest such number?".
Since the conditions given does not have a unique solution, "Data inadequate" should be the correct answer.
(3)
Nilesh said:
3 years ago
Why p=26 taken? Please explain the answer.
(2)
CHETHAN said:
4 years ago
How P = 26?
Pleas explain.
Pleas explain.
(2)
Satya said:
5 years ago
13p + 11 = 17q + 9.
q = (2 + 13p)/17.
To find the least value of p for which q = (2 + 13p)/17 is a whole number; The divisor must completely divide the dividend.
( i.e. denominator must completely divide the numerator.)
So the possible dividends are 170, 340, 510, ....
With Dividend 170,
(2 + 13p) = 170------------> p = 12.9..... , i.e. a fraction.
With dividend 340,
(2 + 13p) = 340 ------------> p = 26 i.e. a whole number.
q = (2 + 13p)/17.
To find the least value of p for which q = (2 + 13p)/17 is a whole number; The divisor must completely divide the dividend.
( i.e. denominator must completely divide the numerator.)
So the possible dividends are 170, 340, 510, ....
With Dividend 170,
(2 + 13p) = 170------------> p = 12.9..... , i.e. a fraction.
With dividend 340,
(2 + 13p) = 340 ------------> p = 26 i.e. a whole number.
(2)
Shahbaj said:
5 years ago
26 is a number by which if we use in a equation of q it is completely divisible by 17.
q=2+13(26) /17=20 that's why we take p=26.
Similarly if we put q=20 in eq.
P=17(20) -2/13=26,
So in both way
X=13(26) +1=349.
Y=17(20) +9=349.
q=2+13(26) /17=20 that's why we take p=26.
Similarly if we put q=20 in eq.
P=17(20) -2/13=26,
So in both way
X=13(26) +1=349.
Y=17(20) +9=349.
(2)
Kritesh Kumar said:
4 years ago
9 and 26 are the no's From which if we use it in an equation it will be divisible by 17.
So In this case, we can also use 9 as it is the least one, so 128 could be the answer, but there is no option for 128 that's why they have taken 26 as the least one and obtained the answer as 349.
Correct me if I am wrong.
So In this case, we can also use 9 as it is the least one, so 128 could be the answer, but there is no option for 128 that's why they have taken 26 as the least one and obtained the answer as 349.
Correct me if I am wrong.
(1)
Surya said:
4 years ago
How can we get p value? Please explain.
(1)
Puja said:
8 years ago
One of the easy ways is check options.
349-11 = 338,
Now,338/13 = 26,
Also,349-9 = 340,
340/17 = 20.
Hence from checking opt. B it is right option.
I hope it is clear to all.
349-11 = 338,
Now,338/13 = 26,
Also,349-9 = 340,
340/17 = 20.
Hence from checking opt. B it is right option.
I hope it is clear to all.
(1)
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers