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Math Expert V
Joined: 02 Sep 2009
Posts: 58434
The ages of all children in Group A are the same, and the ages of all  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 78% (01:38) correct 22% (01:54) wrong based on 59 sessions

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Competition Mode Question

The ages of all children in Group A are the same, and the ages of all children in Group B are the same. Is the age of a child in Group A less than the age of a child in Group B?

(1) The sum of the ages of 3 children in Group A and 2 children in Group B is less than the sum of ages of 2 children in Group A and 4 children in Group B.

(2) The sum of the ages of 4 children in Group A and 3 children in Group B is less than the sum of ages of 3 children in Group A and 4 children in Group B.

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Re: The ages of all children in Group A are the same, and the ages of all  [#permalink]

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Let's define as follows:
age of every child in Group A = a
age of every child in Group B = b

Q. a < b?

(1) 3a + 2b < 2a + 4b
--> a < 2b
If a=3, b=4, then a < 2b and a < b (ok)
If a=3, b=2, then a < 2b but a > b (no)
NOT SUFFICIENT

(2) 4a + 3b < 3a + 4b
--> a < b. This statement exactly addresses the question
SUFFICIENT

Originally posted by chondro48 on 22 Aug 2019, 07:12.
Last edited by chondro48 on 22 Aug 2019, 07:32, edited 3 times in total.
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Re: The ages of all children in Group A are the same, and the ages of all  [#permalink]

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1
The ages of all children in Group A are the same, and the ages of all children in Group B are the same. Is the age of a child in Group A less than the age of a child in Group B?

(1) The sum of the ages of 3 children in Group A and 2 children in Group B is less than the sum of ages of 2 children in Group A and 4 children in Group B.

(2) The sum of the ages of 4 children in Group A and 3 children in Group B is less than the sum of ages of 3 children in Group A and 4 children in Group B.

group A ; x and group B ; y
so to determine whether y>x?
#1The sum of the ages of 3 children in Group A and 2 children in Group B is less than the sum of ages of 2 children in Group A and 4 children in Group B.
3x+2y<2x+4y
x<2y insufficient
#2
The sum of the ages of 4 children in Group A and 3 children in Group B is less than the sum of ages of 3 children in Group A and 4 children in Group B.
4x+3y<3x+4y
we get ; x<y ; sufficient
IMO B

Originally posted by Archit3110 on 22 Aug 2019, 07:37.
Last edited by Archit3110 on 22 Aug 2019, 07:46, edited 1 time in total.
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Re: The ages of all children in Group A are the same, and the ages of all  [#permalink]

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IMO-B

Let Age of childrens in Grp A= x & Grp= y

Statement 1:
3x + 2y < 2x + 4y = x < 2y -------Not sufficient

Statement 2:
4x + 3y < 3x + 4y
x < y
Sufficient
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Re: The ages of all children in Group A are the same, and the ages of all  [#permalink]

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1
Quote:
The ages of all children in Group A are the same, and the ages of all children in Group B are the same. Is the age of a child in Group A less than the age of a child in Group B?

(1) The sum of the ages of 3 children in Group A and 2 children in Group B is less than the sum of ages of 2 children in Group A and 4 children in Group B.

(2) The sum of the ages of 4 children in Group A and 3 children in Group B is less than the sum of ages of 3 children in Group A and 4 children in Group B.

Given: The ages of all children in Group A are the same, and the ages of all children in Group B are the same.

Asked: Is the age of a child in Group A less than the age of a child in Group B?

Let the age of a child in Group A be a and in Group B be b.

Q. a<b?

(1) The sum of the ages of 3 children in Group A and 2 children in Group B is less than the sum of ages of 2 children in Group A and 4 children in Group B.
3a + 2b < 2a + 4b
a < 2b > b
NOT SUFFICIENT

(2) The sum of the ages of 4 children in Group A and 3 children in Group B is less than the sum of ages of 3 children in Group A and 4 children in Group B.
4a + 3b < 3a + 4b
a < b
SUFFICIENT

IMO B
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Re: The ages of all children in Group A are the same, and the ages of all  [#permalink]

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The ages of all children in Group A are the same, and the ages of all children in Group B are the same. Is the age of a child in Group A less than the age of a child in Group B?

(1) The sum of the ages of 3 children in Group A and 2 children in Group B is less than the sum of ages of 2 children in Group A and 4 children in Group B.

(2) The sum of the ages of 4 children in Group A and 3 children in Group B is less than the sum of ages of 3 children in Group A and 4 children in Group B.

Let age of children in group A = A
Age of children in group B = B

A < B ?

Statement 1) 3A + 2B < 2A + 4B
 3A – 2A < 4B – 2B
 A < 2B

Hence A > B or A < B

INSUFFICIENT.

Statement 2) 4A + 3B < 3A + 4B
 4A – 3A < 4B – 3B
 A < B

SUFFICIENT

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Senior Manager  G
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Re: The ages of all children in Group A are the same, and the ages of all  [#permalink]

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From question stem all children in Grp A have the same age, say A,and all children in Grp B have the same age, say B.

From statement 1, 3A+2B<2A+4B
Meaning A<2B. Not sufficient since if A=4, and B=3,A>B although A<2B. And if A=4 and B=5, A<B and A<2B.

From 2, 4A+3B<3A+4B
Meaning A<B.
This is sufficient since we can answer yes, that a child in Group A has an age less than that in Grp in Grp B.

Answer is therefore B.

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Re: The ages of all children in Group A are the same, and the ages of all  [#permalink]

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This question is easy to understand if you plot point on Number line and check average and weigh which side will be more if positions or weight is altered.
IMO :D
Lets see what OA says.
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Re: The ages of all children in Group A are the same, and the ages of all  [#permalink]

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Ans- B
option B tells A<B hence sufficient
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Re: The ages of all children in Group A are the same, and the ages of all  [#permalink]

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IMO B is the answer
Let age of each student in GRP A= 'A' & in GRP B = 'B'
cond 1 states that - 3A +2B < 2A+ 4B
ON SOLVING
A<2B - THUS THIS DOESN'T TELL US THE RELATION BETWEEN A & B AS IF (A,B) = (3,2) OR (2,3)
cond 2 states that 4A+3B < 3A+4B
ON SOLVING WE GET
A<B
Hence B alone is sufficient to answer the question.

Thanks
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Senior Manager  G
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Re: The ages of all children in Group A are the same, and the ages of all  [#permalink]

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Group A={a,a,a,a...}
-> Let ' a ' be the age of a child

Group B={b,b,b,b...}
-> Let ' b ' be the age of a child

is a< b ??

Statement1:
3a+ 2b<2a+4b
--> a<2b
NO info about what a and b are:
if a=3 and 2b=8, then a< b (yes)
if a=3 and 2b=4, then a> b (no)
--> insufficient

Statement2:
4a+ 3b< 3a+4b
a< b
--> Sufficient

The answer is B.
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Re: The ages of all children in Group A are the same, and the ages of all  [#permalink]

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The ages of all children in Group A are the same, and the ages of all children in Group B are the same. Is the age of a child in Group A less than the age of a child in Group B?
Age of children in Group A = x, Age of children in Group B = y.
Is x < y ?

(1) The sum of the ages of 3 children in Group A and 2 children in Group B is less than the sum of ages of 2 children in Group A and 4 children in Group B.
--> 3x+2y < 2x+4y
--> x<2y
--> (i) assume x = 7 yrs and y = 4 yrs
--> 7 < 2*(4) --> however, x is not less than y
--> (ii) assume x = 2 yrs and y = 4 yrs
--> 2 < 2*(4) --> however, x is less than y
no unique solution, so Answer is not A

(2) The sum of the ages of 4 children in Group A and 3 children in Group B is less than the sum of ages of 3 children in Group A and 4 children in Group B.
--> 4x+3y < 3x+4y
--> x<y and this is what the question asks..
--> so, definitely x<y
B is the Answer Re: The ages of all children in Group A are the same, and the ages of all   [#permalink] 23 Aug 2019, 06:12
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