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If Father's age is 1 less than twice the son's age, what is

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If Father's age is 1 less than twice the son's age, what is [#permalink] New post   Updated on: 31 Jan 2012, 13:24
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If Father's age is 1 less than twice the son's age, what is the son's age?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM.
(2) Father is at least 25 years older than son
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A

Originally posted by docabuzar on 31 Jan 2012, 04:50.
Last edited by docabuzar on 31 Jan 2012, 13:24, edited 1 time in total.
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If Father's age is 1 less than twice the son's age, what is [#permalink] New post   31 Jan 2012, 06:02
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docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?
A. The digits MN making up the father's age are reversed in the son's age i.e NM.
B. Father is at least 25 years older than son

I m not sure of the answer but i think its "A"


Given: F+1=2S. Question: S=?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM --> F=10M+N and S=10N+M (notice that M and N must be digits: 0, 1, 2, ..., 9) --> (10M+N)+1=2*(10N+M) --> 8M=19N-1. Only one set of digits satisfy this equation: M=7 and N=3 (by trial and error: 19N-1 is even and also a multiple of 8 --> N must odd --> so try N=1 and N=3 to see whether 19N-1 is a multiple of 8. For N>=5, M>10 so not a solution for M as it must be a single digit integer) --> S=10N+M=37 and F=73. Sufficient.

(2) Father is at least 25 years older than son. Clearly insufficient: F=63 and S=36 or F=73 and S=37 .

Answer: A.

Hope it's clear.
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Re: If Father's age is 1 less than twice the son's age, what is [#permalink] New post   01 Feb 2012, 02:26
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docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?
A. The digits MN making up the father's age are reversed in the son's age i.e NM.
B. Father is at least 25 years older than son

I m not sure of the answer but i think its "A"

Gimme Kudos if you like the question


Look at the big picture. You can solve this question quickly using intuition.

Father's age is almost as much as twice of son's age. (just 1 less)
Son's age = NM, Father's age = MN

Say, son's age is 12 then father's is 21 (3 less than twice)
Say, son's age is 13 then father's is 31 (much more than twice)
I hope you understand that you can give up on the 10s series here because the gap will keep widening (diff b/w 14 and 41 will be even more)

Say, son's age is 24 then father's is 42 (much less than twice)
Say, son's age is 25, then father's is 52 (more than twice so give up on the 20s series too)

Say son's age is 36, then father's is 63 (much less than twice)
Say son's age is 37, then father's is 73 (1 less than twice. Got it!)

It's easy to say that there will be no other such combination because 49, 94 doesn't work. Nothing in 50s, 60s and so on will work because we need to stick to 2 digit numbers.

Hence, only statement 1 is sufficient.
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Re: If Father's age is 1 less than twice the son's age, what is [#permalink] New post   31 Jan 2012, 22:00
Its all in the wording. Father is 1 less than twice of son, so in other words twice of son is 1 more than father

F = 2S -1

Had it been like " Father is 1 more than twice the son " then F=2S+1 or F-1=2S.

Hope I have added some thing.
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Re: If Father's age is 1 less than twice the son's age, what is [#permalink] New post   01 Feb 2012, 00:05
docabuzar wrote:
Its all in the wording. Father is 1 less than twice of son, so in other words twice of son is 1 more than father

F = 2S -1

Had it been like " Father is 1 more than twice the son " then F=2S+1 or F-1=2S.

Hope I have added some thing.


Hey thanks for the explanation. I just messed up with the words.
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If Father's age is 1 less than twice the son's age, what is [#permalink] New post   01 Feb 2012, 02:30
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subhajeet wrote:
Bunuel wrote:
docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?
A. The digits MN making up the father's age are reversed in the son's age i.e NM.
B. Father is at least 25 years older than son

I m not sure of the answer but i think its "A"


Given: F+1=2S. Question: S=?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM --> F=10M+N and S=10N+M (notice that M and N must be digits: 0, 1, 2, ..., 9) --> (10M+N)+1=2*(10N+M) --> 8M=19N-1. Only one set of digits satisfy this equation: M=7 and N=3 (by trial and error: 19N-1 is even and also a multiple of 8 --> N must odd --> so try N=1 and N=3 to see whether 19N-1 is a multiple of 8. For N>=5, M>10 so not a solution for M as it must be a single digit integer) --> S=10N+M=37 and F=73. Sufficient.

(2) Father is at least 25 years older than son. Clearly insufficient: F=63 and S=36 or F=73 and S=37 .

Answer: A.

Hope it's clear.


Bunnel: will the equation here not be F-1 =2S ( Father's age is 1 less than twice the son's age)


It's all about word translation: father's age is 1 less than twice the son's age, so F is less than 2S by 1 --> so we need to add 1 to F to get 2S --> F+1=2S.

Hope it's clear
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If Father's age is 1 less than twice the son's age, what is [#permalink] New post   23 Dec 2016, 16:08
Bunuel wrote:
docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?
A. The digits MN making up the father's age are reversed in the son's age i.e NM.
B. Father is at least 25 years older than son

I m not sure of the answer but i think its "A"


Given: F+1=2S. Question: S=?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM --> F=10M+N and S=10N+M (notice that M and N must be digits: 0, 1, 2, ..., 9) --> (10M+N)+1=2*(10N+M) --> 8M=19N-1. Only one set of digits satisfy this equation: M=7 and N=3 (by trial and error: 19N-1 is even and also a multiple of 8 --> N must odd --> so try N=1 and N=3 to see whether 19N-1 is a multiple of 8. For N>=5, M>10 so not a solution for M as it must be a single digit integer) --> S=10N+M=37 and F=73. Sufficient.

(2) Father is at least 25 years older than son. Clearly insufficient: F=63 and S=36 or F=73 and S=37 .

Answer: A.

Hope it's clear.


Hello can you elaborate if it is possible? how did we come up with F=10M+N and S=10N+M , Basically i understood how u solved it but i cannot comprehend the way we approach it initially

Thank you in advance
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Re: If Father's age is 1 less than twice the son's age, what is [#permalink] New post   24 Dec 2016, 00:55
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stampap wrote:
Bunuel wrote:
docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?
A. The digits MN making up the father's age are reversed in the son's age i.e NM.
B. Father is at least 25 years older than son

I m not sure of the answer but i think its "A"


Given: F+1=2S. Question: S=?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM --> F=10M+N and S=10N+M (notice that M and N must be digits: 0, 1, 2, ..., 9) --> (10M+N)+1=2*(10N+M) --> 8M=19N-1. Only one set of digits satisfy this equation: M=7 and N=3 (by trial and error: 19N-1 is even and also a multiple of 8 --> N must odd --> so try N=1 and N=3 to see whether 19N-1 is a multiple of 8. For N>=5, M>10 so not a solution for M as it must be a single digit integer) --> S=10N+M=37 and F=73. Sufficient.

(2) Father is at least 25 years older than son. Clearly insufficient: S=25 and N=13 or S=27 and N=14 .

Answer: A.

Hope it's clear.


Hello can you elaborate if it is possible? how did we come up with F=10M+N and S=10N+M , Basically i understood how u solved it but i cannot comprehend the way we approach it initially

Thank you in advance


This is a way of writing a two-digit number. Any two-digit integer can be represented as 10a+b (where a and b are single digit integers), for example 37=3*10+7, 88=8*10+8, etc.
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Re: If Father's age is 1 less than twice the son's age, what is [#permalink] New post   24 Dec 2016, 07:16
Oh yes! silly me , i had completely forgot it , now its clear!

thank you bunuel
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Re: If Father's age is 1 less than twice the son's age, what is [#permalink] New post   15 Mar 2020, 19:22
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docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM.
(2) Father is at least 25 years older than son


1) 10M + N = 2(10N + M) -1
10M + N =20N + 2M -1
8M = 19N -1
19N - 8M = 1
N and M both can assume integer value between 1 to 9. So, the highest value 8M can take is 72. To make this statement true, N has to be 3 and M has to be 7 only. No other integer will make the statement true. SUFFICIENT.

2) Father's age can be any odd number greater or equal to 51 to make this statement true. Not sufficient.
A is the answer.
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Re: If Father's age is 1 less than twice the son's age, what is [#permalink] New post   05 Jun 2020, 02:38
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Bunuel wrote:
docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?
A. The digits MN making up the father's age are reversed in the son's age i.e NM.
B. Father is at least 25 years older than son

I m not sure of the answer but i think its "A"


Given: F+1=2S. Question: S=?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM --> F=10M+N and S=10N+M (notice that M and N must be digits: 0, 1, 2, ..., 9) --> (10M+N)+1=2*(10N+M) --> 8M=19N-1. Only one set of digits satisfy this equation: M=7 and N=3 (by trial and error: 19N-1 is even and also a multiple of 8 --> N must odd --> so try N=1 and N=3 to see whether 19N-1 is a multiple of 8. For N>=5, M>10 so not a solution for M as it must be a single digit integer) --> S=10N+M=37 and F=73. Sufficient.

(2) Father is at least 25 years older than son. Clearly insufficient: S=25 and N=13 or S=27 and N=14 .

Answer: A.

Hope it's clear.


Bunuel in your statement #2, shouldn't "S" be "F" (Father), and "N" be "S" (Son)?
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Re: If Father's age is 1 less than twice the son's age, what is [#permalink] New post   05 Jun 2020, 02:55
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stepharr wrote:

Bunuel in your statement #2, shouldn't "S" be "F" (Father), and "N" be "S" (Son)?


Yes, it should have been: (2) Father is at least 25 years older than son. Clearly insufficient: F=63 and S=36 or F=73 and S=37.

Thank you. Edited.
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Re: If Father's age is 1 less than twice the son's age, what is [#permalink] New post   05 Jun 2020, 04:40
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docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM.
(2) Father is at least 25 years older than son


Asked: If Father's age is 1 less than twice the son's age, what is the son's age?

Let f be father's age and s be son's age.
f = 2s - 1; s=?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM.
f= 10M + N
s = 10N + M
10M + N = 2(10N + M) - 1 = 20 N + 2M - 1
8M = 19N - 1
N = (8M + 1)/19
(M,N) = (7,3)
s = 37 = Son's age
SUFFICIENT

(2) Father is at least 25 years older than son
f >= s + 25
2s - 1 >= s + 25
s >=26
NOT SUFFICIENT

IMO A
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Re: If Father's age is 1 less than twice the son's age, what is [#permalink] New post   05 Jun 2020, 07:16
docabuzar wrote:
If Father's age is 1 less than twice the son's age, what is the son's age?

(1) The digits MN making up the father's age are reversed in the son's age i.e NM.
(2) Father is at least 25 years older than son


given
F = 2S-1
find S ;
#1
The digits MN making up the father's age are reversed in the son's age i.e NM.
10a+b=10b+a
10a+b=20b+2a-1
8a=19b-1
8a+1=19b
for a = 7 and b = 3
so father is 73 and Son ; 37
sufficient
#2
Father is at least 25 years older than son
F=2s-1
26 = 2s
s= 13
least Son is 13 and Father = 25
son = 14 ; father = 27
many possibilities
insufficient
OPTION A
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Re: If Father's age is 1 less than twice the son's age, what is [#permalink] New post   14 Apr 2024, 10:21
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