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Each of the question below consists of a question and three statements number I, II and III given below it. You have to decide whether the data provided in the statement are sufficient to answer the question. A bag contains some number of Diamond of 4 different colors (Red, Pink, blue and yellow). What is the total number of Diamond in the bag? I. If 5 Pink Diamond from the bag are replaced by Yellow Diamond, Then the ratio of probabilities of picking 2 yellow Diamond at a time to picking 3 Blue Diamond at a time becomes (1/116). II. The different between probabilities of picking 2 Red Diamonds at a time and probability of picking 2 Blue Diamonds at a time is (23/330). III. If a Diamond is picked from the bag, then there is 40% chance that it is a red Diamond. Probability of picking 2 Red Diamond from the bag is (26/165).

Each of the question below consists of a question and three statements number I, II and III given below it. You have to decide whether the data provided in the statement are sufficient to answer the question. A bag contains some number of Diamond of 4 different colors (Red, Pink, blue and yellow). What is the total number of Diamond in the bag? I. If 5 Pink Diamond from the bag are replaced by Yellow Diamond, Then the ratio of probabilities of picking 2 yellow Diamond at a time to picking 3 Blue Diamond at a time becomes (1/116). II. The different between probabilities of picking 2 Red Diamonds at a time and probability of picking 2 Blue Diamonds at a time is (23/330). III. If a Diamond is picked from the bag, then there is 40% chance that it is a red Diamond. Probability of picking 2 Red Diamond from the bag is (26/165). Correct Answer The data in only statement III alone is sufficient to answer the question.

From Statement I:

Let number of Red, Pink, Blue and Yellow Diamond in the bag be P, Q, R and S respectively.

Let total number of diamond in the bag be T

T = (P + Q + R + S)

After replacing 5 Pink Diamond by Yellow diamond.

Probability of picking 2 Yellow diamond =

((S + 5 )C2)/ (TC2) = ((S + 5) × (S + 4))/ (T × (T – 1))

Probability of packing 3 Blue diamond

= ((R)C2)/ (TC2)

= (R × (R - 1) × (R - 2))/ (T × (T – 1) × (T – 2))

The ratio of probabilities of picking 2 Yellow diamond at a time to picking 3 Blue diamond at a time

= (((S + 5) × (S + 4))/ (T × (T - 1)))/( (R × (R – 1) × (R – 2))/(T × (T – 1) × (T – 2)))

= (((S + 5) × (S + 4) × (T – 2))/(R × (R – 1) × (R – 2))) = (1/116)

⇒ 116 × (S + 5) × (S + 4) × ((T – 2) = (R × (R – 1) × (R – 2))

⇒ 116 × (S + 5) × (S + 4) × ((T – 2) = (R × (R – 1) × (R – 2))

So, data in statement I alone is not sufficient to answer the question.

From Statement II:

Let number of Red diamonds and number of Blue diamonds in the bag be P and R respectively.

Lets total number of diamond be T

Probability of picking 2 Red diamonds = (pC2)/ (TC2)

= (P × (P – 1))/ (T × (T – 1))

Probability of picking 2 Blue diamonds =

(RC2)/ (TC2) = (R × (R – 1))/ (T × (T – 1))

As per given,

((P × (P – 1))/ (T × (T – 1))) – ((R × (R – 1)) / (T × (T – 1))) = (23/330)

((P × (P – 1)) - (R × (R – 1))) = (23/330) × (T × (T – 1))

So, data in statement II alone is not sufficient to answer the question.

Even combining data from statement I and II together is also not sufficient to answer the question.

From Statement III:

Probability of picking a red diamond = (Number of red diamond)/ (Total number of diamond)

= (40/100) = (2/5)

So, let number of red diamond be 2T and total number of diamond be 5T

Probability of picking 2 red diamond from the bag

= (2TC2)/(5TC2)

= (2T × (2T – 1))/ (5T × (5T -1)) = (26/165)

(4T2 – 2T)/ (25T2 – 5T) = (26/165)

660T2 – 330T = 650T2 – 130T

10T2 = 200T

T = 20

Total number of diamonds in the bag is 100.

Data in statement III alone is sufficient to answer the question.

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