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Number of Male Offspring: 4
Number of female offspring: 3
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Difficulty:
55%
(hard)
Question Stats:
60% (02:07) correct
40%
(02:16)
wrong
based on 1462
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The biological offspring of Arianna and Noah are such that each male has the same number of brothers as sisters, and each female has half as many sisters as brothers.
Based on the information provided, select for "Number of male offspring" the number of male offspring of Arianna and Noah and select for "Number of female offspring" the number of female offspring of Arianna and Noah. Make only two selections, one in each coloumn.
Based on the information provided, select for "Number of male offspring" the number of male offspring of Arianna and Noah and select for "Number of female offspring" the number of female offspring of Arianna and Noah. Make only two selections, one in each coloumn.
| Number of Male Offspring | Number of female offspring | |
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 |
ShowHide Answer
Official Answer
Number of Male Offspring: 4
Number of female offspring: 3
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22 Jan 2024, 04:54
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The biological offspring of Arianna and Noah are such that
each male has the same number of brothers as sisters,=> Say Mr A has x brothers and x sisters. Thus F=x annd M=x+1(Mr A)
each female has half as many sisters as brothers. => Say Ms B has y brothers and y/2 sisters. Thus M=y and F=1(Mrs B)+y/2
Thus, equations we have
\(F=x=1+\frac{y}{2}…….y=2x-2\)
\(M=x+1=y\)
Equate the two => \(x+1 = 2x-2……..x=3\)
Thus females are 3 and males are x+1 or 4.
each male has the same number of brothers as sisters,=> Say Mr A has x brothers and x sisters. Thus F=x annd M=x+1(Mr A)
each female has half as many sisters as brothers. => Say Ms B has y brothers and y/2 sisters. Thus M=y and F=1(Mrs B)+y/2
Thus, equations we have
\(F=x=1+\frac{y}{2}…….y=2x-2\)
\(M=x+1=y\)
Equate the two => \(x+1 = 2x-2……..x=3\)
Thus females are 3 and males are x+1 or 4.
22 Jan 2024, 09:36
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Alternative Approach
The biological offspring of Arianna and Noah are such that each male has the same number of brothers as sisters, and each female has half as many sisters as brothers.
Based on the information provided, select for "Number of male offspring" the number of male offspring of Arianna and Noah and select for "Number of female offspring" the number of female offspring of Arianna and Noah. Make only two selections, one in each column.
1
2
3
4
5
Since "each female has half as many sisters as brothers," there must be an even number of male offspring. After all, only integer numbers of sisters and brothers can exist, and half of a number is an integer only if that number is even.
So, of the answer choices, the only possible numbers of male offspring are 2 and 4.
Try 2 male offspring.
each male has the same number of brothers as sisters
2 males
Each 1 male has 1 brother and thus has 1 sister.
each female has half as many sisters as brothers
If each male has just 1 sister, then there is just one female, and the female has 0 sisters.
0 is not half of 2.
Eliminate 2 as a possible number of male offspring.
Try 4 male offspring.
each male has the same number of brothers as sisters
4 males
Each of the 4 males has 3 brothers and thus has 3 sisters.
each female has half as many sisters as brothers
If each male has 3 sisters, there are 3 female offspring, and each female has 2 sisters.
2 is half of of 4.
Perfect.
Correct Answer: 4, 3
The biological offspring of Arianna and Noah are such that each male has the same number of brothers as sisters, and each female has half as many sisters as brothers.
Based on the information provided, select for "Number of male offspring" the number of male offspring of Arianna and Noah and select for "Number of female offspring" the number of female offspring of Arianna and Noah. Make only two selections, one in each column.
1
2
3
4
5
Since "each female has half as many sisters as brothers," there must be an even number of male offspring. After all, only integer numbers of sisters and brothers can exist, and half of a number is an integer only if that number is even.
So, of the answer choices, the only possible numbers of male offspring are 2 and 4.
Try 2 male offspring.
each male has the same number of brothers as sisters
2 males
Each 1 male has 1 brother and thus has 1 sister.
each female has half as many sisters as brothers
If each male has just 1 sister, then there is just one female, and the female has 0 sisters.
0 is not half of 2.
Eliminate 2 as a possible number of male offspring.
Try 4 male offspring.
each male has the same number of brothers as sisters
4 males
Each of the 4 males has 3 brothers and thus has 3 sisters.
each female has half as many sisters as brothers
If each male has 3 sisters, there are 3 female offspring, and each female has 2 sisters.
2 is half of of 4.
Perfect.
Correct Answer: 4, 3
