Ann bought five different kinds of fruit: apples, oranges, pears

Ann bought five different kinds of fruit: apples, oranges, pears, mangoes, and bananas. If the number of apples that Ann bought was twice the number of oranges and if the number of pears that Ann bought was the same as the number of apples and oranges combined, what fraction of the total number of pieces of fruit that Ann bought were pears?

(1) Ann bought a total of 18 pieces of fruit.
(2) Ann bought 5 bananas

Let us assume 'x' be the number of oranges bought by Ann.
A (apples) -> 2x,O(oranges)->x,P(Pears)->3x,M(Mangos)->Not known,B(Bananas)-> Not Known

Option (1)
Even if we know the total number of pieces of fruit (18 i.e given),it will be required to find the number of quantities of anyone of Apples,Oranges or Pears (as we can derive 'x' based on the value).It is not possible to calculate 3x/18 (as we do not know the value of 'x')
Not Sufficient
Option (2)
In this option as well,we have been given the value of (bananas) B=5 that makes it impossible to evaluate the fraction of total number of pieces of pears.First off all we do not know the total number of quantities of fruit and secondly number of quantities of anyone of Apples,Oranges or pears is unknown.
Not Sufficient.
Option (1) + (2).
Even if we know the total number of pieces of fruit (option 1) and quantity of bananas (B=5)(Option 2) available,it will be still required to find the number of quantities of anyone of Apples,Oranges or Pears (as we can derive 'x' based on the value).It is not possible to calculate 3x/18 (as we do not know the value of 'x').
Not Sufficient.

Hence Option 'E' .

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Ann bought five different kinds of fruit: apples, oranges, pears, mangoes, and bananas. If the number of apples that Ann bought was twice the number of oranges and if the number of pears that Ann bought was the same as the number of apples and oranges combined, what fraction of the total number of pieces of fruit that Ann bought were pears?

(1) Ann bought a total of 18 pieces of fruit.
(2) Ann bought 5 bananas.

We have 5 variables (a,o,p,m,b) and 2 equations (a=2o, p=a+o) in the original condition, but only 2 equations are given by the conditions, so there is high chance (E) will be the answer.
Looking at the conditions together, a+o+p+m+b=18, b=5, but a=2o, p=a+o=3o still does not give the number of p, so is insufficient, making the answer (E).

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

oranges = r
apples = 2r
pear = a+r = 3r

Ratio to be found = 3r /(r+2r+3r+M+B) = 3r /(6r+M+B) ??

(1) 3r/18. r is unknown. Insufficient

(2) B =5, So 3r /(6r+M+5) cannot be calculated. Insufficient

(1)+(2), 6r+M+5 = 18;
6r + M = 13. still the ratio is terms of 'r' and 'M' which cannot be calculated. Insufficient

E is correct.

To determine the fraction of the total number of pieces of fruit that Ann bought were pears, let's analyze the given information.

Let's assign variables to represent the quantities of each fruit that Ann bought:
Let A represent the number of apples.
Let O represent the number of oranges.
Let P represent the number of pears.
Let M represent the number of mangoes.
Let B represent the number of bananas.

We are given the following information:

The number of apples that Ann bought was twice the number of oranges:
A = 2O

The number of pears that Ann bought was the same as the number of apples and oranges combined:
P = A + O

Now, let's analyze each statement:

Statement (1) states that Ann bought a total of 18 pieces of fruit.
This gives us the equation: A + O + P + M + B = 18

Statement (2) states that Ann bought 5 bananas.
This gives us the equation: B = 5

Now, let's solve the problem step by step using these statements:

From the given information, we have:
A = 2O (equation 1)
P = A + O (equation 2)
B = 5 (equation 3)

To determine the fraction of the total number of pieces of fruit that Ann bought were pears, we need to find the value of P in terms of the total number of fruit pieces.

Substituting equation 1 into equation 2:
P = (2O) + O
P = 3O

Substituting equation 3 into the equation from Statement (1):
A + O + P + M + 5 = 18

Substituting A = 2O and P = 3O:
2O + O + 3O + M + 5 = 18
6O + M + 5 = 18
6O + M = 13

Now, we have two equations:
P = 3O (equation 4)
6O + M = 13 (equation 5)

Since we have two equations and three unknowns (O, P, and M), we cannot determine the exact values of O, P, and M. Therefore, we cannot determine the fraction of the total number of pieces of fruit that Ann bought were pears.

Hence, the answer is that we cannot determine the fraction based on the given information in statements (1) and (2).