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Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation PDF Download

There are nine boxes arranged in a 3×3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.
The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same.
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation
Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied.
(i) The minimum among the numbers of coins in the three sacks in the box is 1.
(ii) The median of the numbers of coins in the three sacks is 1.
(iii) The maximum among the numbers of coins in the three sacks in the box is 9.

Q1: What is the total number of coins in all the boxes in the 3rd row?
(a) 36
(b) 30
(c) 15
(d) 45

Ans: (d)

We are given that each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.
The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same.
⇒ The total number of coins in a box range from 3 (1 + 1 + 1) to 27 (9 + 9 + 9)
Since, it is given that the average number of coins per sack in the boxes are all distinct integers ⇒ The total number of coins in a box would be 3, 6, 9, 12, 15, 18, 21, 24, 27 ⇒ averages of 1, 2, 3, 4,....,9 ⇒ Sum = 45.
⇒ Sum of averages coins in a box in a row or column = 45/3 = 15 [The total number of coins in each row is the same. The total number of coins in each column is also the same.] ==> (1)
Let us represent the final configuration of the sacks in boxes as follows:
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationAlso a bag (x, y) => bag in xth row and yth column.
We are given 2 clues ⇒ Table-1 & Table-2
Consider bag (3,1)
⇒ From Table-1 ⇒ Median = 8 & From Table-2 all 3 sacks have more than 5 coins. Also * ⇒ There is a 9 in one of the sacks.
⇒ c, 8, 9 are the coins in bag (3,1), now c > 5 & c + 8 + 9 should be a multiple of 3 ⇒ c = 7 is the only possibility.
⇒ bag (3,1) has 7, 8, 9 coins with average = 8.
Consider bag (2,1)
Median = 2 and 1 sack has more than 5 coins. Also ** ⇒ conditions i & iii should be satisfied
⇒ 1, 2, 9 are the coins in bag (2,1) with average = 4
Consider bag (1,2)
Median = 9 and 2 elements are more than 5. Also * ⇒ (9 is present & 1 is not present)
⇒ c, 9, 9 are the coins in bag (1,2) and c is not equal to 1 and less than 5 ⇒ c = 3 for c + 18 to be a multiple of 3.
⇒ 3, 9, 9 are the coins in bag (1,2) with average = 7.
Capturing this info. in the table:
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationFrom (1), The average in bag (1,1) is 15 - 4 - 8 = 3.
From (1), The average in bag (1,3) is 15 - 3 - 7 = 5.
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationConsider bag (1,1)
Avg. = 3, 1 sack has more than 5 and ** ⇒ 2 conditions are being satisfied. ⇒ (can't be condition-3 ⇒ 9 coins as the total sum of coins is itself 3 * 3 = 9)
⇒ bag (1,1) has 1, 1, 7 coins with average = 3.
Consider bag (1,3)
Avg. = 5 ⇒ Sum = 15.
Median = 6 and 2 sacks have more than 5 and * ⇒ (1 condition is satisfied)
Not condition ii as the median is 6 & Not condition iii as the sum of 2 sacks itself will become 6 + 9 = 15
⇒ 1, 6, c are the coins ⇒ For sum = 15 ⇒ c = 15 - 1 - 6 = 8
⇒ bag (1,3) has 1, 6, 8 coins with average = 5.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Consider bag (3,3)
0 sacks have more than 5 coins and ** ⇒ conditions i & ii are being satisfied.
⇒ 1,1,c are the coins. Now c = 1 or 2 or 3 or 4 ⇒ c = 1 or 4 for number of coins to be a multiple of 3.
But c = 1 as no other bag has the possibility to get avg. = 1 as bag (2,2) should have 1, b, c coins and b and c should be more than 1 as only 1*
⇒ bag (3,3) has 1, 1, 1 coins with average = 1.
Now, we can fill the averages in all the bags.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

In bag (2,3) Avg. = 9 ⇒ 9, 9, 9 are the coins.
In bag (2,2) ⇒ Avg. = 2 ⇒ Sum = 6 and only 1* ⇒ smallest element should be 1.
⇒ 1, b, c are the coins where b + c = 5 and b, c can't be equal to 1 and less than 5 ⇒ 2 + 3 = 5 is the only possibility.
⇒ 1, 2, 3 are the coins with average = 2.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Considering bag (3,2)
Avg. = 6 ⇒ Sum = 18.
2 sacks more than 5 coins and ** ⇒ 2 sacks have 1 and 9 coins.
⇒ bag (3,2) has 1, c, 9 coins and c = 18 - 1 - 9 = 8
⇒ bag (3,2) has 1, 8, 9 coins with average = 6 coins.
==> Final required table, bracket number ⇒ average coins per sack in the bag.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Sum of coins in 3rd row = 8 * 3 + 6 * 3 + 1 * 3 = 45.

Q2:  How many boxes have at least one sack containing 9 coins?
(a) 3
(b) 4
(c) 5
(d) 8

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Ans: (c)
We are given that each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.
The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same.
⇒ The total number of coins in a box range from 3 (1 + 1 + 1) to 27 (9 + 9 + 9)
Since, it is given that the average number of coins per sack in the boxes are all distinct integers ⇒ The total number of coins in a box would be 3, 6, 9, 12, 15, 18, 21, 24, 27 ⇒ averages of 1, 2, 3, 4,....,9 ⇒ Sum = 45.
⇒ Sum of averages coins in a box in a row or column = 45/3 = 15 [The total number of coins in each row is the same. The total number of coins in each column is also the same.] ==> (1)
Let us represent the final configuration of the sacks in boxes as follows:
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationAlso a bag (x, y) => bag in xth row and yth column.
We are given 2 clues ⇒ Table-1 & Table-2
Consider bag (3,1)
⇒ From Table-1 ⇒ Median = 8 & From Table-2 all 3 sacks have more than 5 coins. Also * ⇒ There is a 9 in one of the sacks.
⇒ c, 8, 9 are the coins in bag (3,1), now c > 5 & c + 8 + 9 should be a multiple of 3 ⇒ c = 7 is the only possibility.
⇒ bag (3,1) has 7, 8, 9 coins with average = 8.
Consider bag (2,1)
Median = 2 and 1 sack has more than 5 coins. Also ** ⇒ conditions i & iii should be satisfied
⇒ 1, 2, 9 are the coins in bag (2,1) with average = 4
Consider bag (1,2)
Median = 9 and 2 elements are more than 5. Also * ⇒ (9 is present & 1 is not present)
⇒ c, 9, 9 are the coins in bag (1,2) and c is not equal to 1 and less than 5 ⇒ c = 3 for c + 18 to be a multiple of 3.
⇒ 3, 9, 9 are the coins in bag (1,2) with average = 7.
Capturing this info. in the table:
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationFrom (1), The average in bag (1,1) is 15 - 4 - 8 = 3.
From (1), The average in bag (1,3) is 15 - 3 - 7 = 5.
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationConsider bag (1,1)
Avg. = 3, 1 sack has more than 5 and ** ⇒ 2 conditions are being satisfied. ⇒ (can't be condition-3 ⇒ 9 coins as the total sum of coins is itself 3 * 3 = 9)
⇒ bag (1,1) has 1, 1, 7 coins with average = 3.
Consider bag (1,3)
Avg. = 5 ⇒ Sum = 15.
Median = 6 and 2 sacks have more than 5 and * ⇒ (1 condition is satisfied)
Not condition ii as the median is 6 & Not condition iii as the sum of 2 sacks itself will become 6 + 9 = 15
⇒ 1, 6, c are the coins ⇒ For sum = 15 ⇒ c = 15 - 1 - 6 = 8
⇒ bag (1,3) has 1, 6, 8 coins with average = 5.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Consider bag (3,3)
0 sacks have more than 5 coins and ** ⇒ conditions i & ii are being satisfied.
⇒ 1,1,c are the coins. Now c = 1 or 2 or 3 or 4 ⇒ c = 1 or 4 for number of coins to be a multiple of 3.
But c = 1 as no other bag has the possibility to get avg. = 1 as bag (2,2) should have 1, b, c coins and b and c should be more than 1 as only 1*
⇒ bag (3,3) has 1, 1, 1 coins with average = 1.
Now, we can fill the averages in all the bags.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

In bag (2,3) Avg. = 9 ⇒ 9, 9, 9 are the coins.
In bag (2,2) ⇒ Avg. = 2 ⇒ Sum = 6 and only 1* ⇒ smallest element should be 1.
⇒ 1, b, c are the coins where b + c = 5 and b, c can't be equal to 1 and less than 5 ⇒ 2 + 3 = 5 is the only possibility.
⇒1, 2, 3 are the coins with average = 2.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Considering bag (3,2)
Avg. = 6 ⇒ Sum = 18.
2 sacks more than 5 coins and ** ⇒ 2 sacks have 1 and 9 coins.
⇒ bag (3,2) has 1, c, 9 coins and c = 18 - 1 - 9 = 8
⇒ bag (3,2) has 1, 8, 9 coins with average = 6 coins.
==> Final required table, bracket number ⇒ average coins per sack in the bag.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Bags (2,1), (3,1), (1,2), (3,2), (2,3) have at least 1 sack with 9 coins. ⇒ Total of 5 bags.

Q3: For how many boxes are the average and median of the numbers of coins contained in the three sacks in that box the same?

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Ans: 4
We are given that each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.
The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same.
⇒ The total number of coins in a box range from 3 (1 + 1 + 1) to 27 (9 + 9 + 9)
Since, it is given that the average number of coins per sack in the boxes are all distinct integers ⇒ The total number of coins in a box would be 3, 6, 9, 12, 15, 18, 21, 24, 27 ⇒ averages of 1, 2, 3, 4,....,9 ⇒ Sum = 45.
⇒ Sum of averages coins in a box in a row or column = 45/3 = 15 [The total number of coins in each row is the same. The total number of coins in each column is also the same.] ==> (1)
Let us represent the final configuration of the sacks in boxes as follows:
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationAlso a bag (x, y) => bag in xth row and yth column.
We are given 2 clues ⇒ Table-1 & Table-2
Consider bag (3,1)
⇒ From Table-1 ⇒ Median = 8 & From Table-2 all 3 sacks have more than 5 coins. Also * ⇒ There is a 9 in one of the sacks.
⇒ c, 8, 9 are the coins in bag (3,1), now c > 5 & c + 8 + 9 should be a multiple of 3 ⇒ c = 7 is the only possibility.
⇒ bag (3,1) has 7, 8, 9 coins with average = 8.
Consider bag (2,1)
Median = 2 and 1 sack has more than 5 coins. Also ** ⇒ conditions i & iii should be satisfied
⇒ 1, 2, 9 are the coins in bag (2,1) with average = 4
Consider bag (1,2)
Median = 9 and 2 elements are more than 5. Also * ⇒ (9 is present & 1 is not present)
⇒ c, 9, 9 are the coins in bag (1,2) and c is not equal to 1 and less than 5 ⇒ c = 3 for c + 18 to be a multiple of 3.
⇒ 3, 9, 9 are the coins in bag (1,2) with average = 7.
Capturing this info. in the table:
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationFrom (1), The average in bag (1,1) is 15 - 4 - 8 = 3.
From (1), The average in bag (1,3) is 15 - 3 - 7 = 5.
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationConsider bag (1,1)
Avg. = 3, 1 sack has more than 5 and ** ⇒ 2 conditions are being satisfied. ⇒ (can't be condition-3 ⇒ 9 coins as the total sum of coins is itself 3 * 3 = 9)
⇒ bag (1,1) has 1, 1, 7 coins with average = 3.
Consider bag (1,3)
Avg. = 5 ⇒ Sum = 15.
Median = 6 and 2 sacks have more than 5 and * ⇒ (1 condition is satisfied)
Not condition ii as the median is 6 & Not condition iii as the sum of 2 sacks itself will become 6 + 9 = 15
⇒ 1, 6, c are the coins ⇒ For sum = 15 ⇒ c = 15 - 1 - 6 = 8
⇒ bag (1,3) has 1, 6, 8 coins with average = 5.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Consider bag (3,3)
0 sacks have more than 5 coins and ** ⇒ conditions i & ii are being satisfied.
⇒ 1,1,c are the coins. Now c = 1 or 2 or 3 or 4 ⇒ c = 1 or 4 for number of coins to be a multiple of 3.
But c = 1 as no other bag has the possibility to get avg. = 1 as bag (2,2) should have 1, b, c coins and b and c should be more than 1 as only 1*
⇒ bag (3,3) has 1, 1, 1 coins with average = 1.
Now, we can fill the averages in all the bags.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

In bag (2,3) Avg. = 9 ⇒ 9, 9, 9 are the coins.
In bag (2,2) ⇒ Avg. = 2 ⇒ Sum = 6 and only 1* ⇒ smallest element should be 1.
⇒ 1, b, c are the coins where b + c = 5 and b, c can't be equal to 1 and less than 5 ⇒ 2 + 3 = 5 is the only possibility.
⇒1, 2, 3 are the coins with average = 2.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Considering bag (3,2)
Avg. = 6 ⇒ Sum = 18.
2 sacks more than 5 coins and ** ⇒ 2 sacks have 1 and 9 coins.
⇒ bag (3,2) has 1, c, 9 coins and c = 18 - 1 - 9 = 8
⇒ bag (3,2) has 1, 8, 9 coins with average = 6 coins.
==> Final required table, bracket number ⇒ average coins per sack in the bag.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Average = Median in boxes (3,1), (2,2), (2,3) and (3,3) ⇒ 4 boxes.

Q4: How many sacks have exactly one coin?

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Ans: 9
We are given that each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.
The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same.
⇒ The total number of coins in a box range from 3 (1 + 1 + 1) to 27 (9 + 9 + 9)
Since, it is given that the average number of coins per sack in the boxes are all distinct integers ⇒ The total number of coins in a box would be 3, 6, 9, 12, 15, 18, 21, 24, 27 ⇒ averages of 1, 2, 3, 4,....,9 ⇒ Sum = 45.
⇒ Sum of averages coins in a box in a row or column = 45/3 = 15 [The total number of coins in each row is the same. The total number of coins in each column is also the same.] ==> (1)
Let us represent the final configuration of the sacks in boxes as follows:
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationAlso a bag (x, y) ⇒ bag in xth row and yth column.
We are given 2 clues ⇒ Table-1 & Table-2
Consider bag (3,1)
⇒ From Table-1 ⇒ Median = 8 & From Table-2 all 3 sacks have more than 5 coins. Also * ⇒ There is a 9 in one of the sacks.
⇒ c, 8, 9 are the coins in bag (3,1), now c > 5 & c + 8 + 9 should be a multiple of 3 ⇒ c = 7 is the only possibility.
⇒ bag (3,1) has 7, 8, 9 coins with average = 8.
Consider bag (2,1)
Median = 2 and 1 sack has more than 5 coins. Also ** ⇒ conditions i & iii should be satisfied
⇒ 1, 2, 9 are the coins in bag (2,1) with average = 4
Consider bag (1,2)
Median = 9 and 2 elements are more than 5. Also * ⇒ (9 is present & 1 is not present)
⇒ c, 9, 9 are the coins in bag (1,2) and c is not equal to 1 and less than 5 ⇒ c = 3 for c + 18 to be a multiple of 3.
⇒ 3, 9, 9 are the coins in bag (1,2) with average = 7.
Capturing this info. in the table:
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationFrom (1), The average in bag (1,1) is 15 - 4 - 8 = 3.
From (1), The average in bag (1,3) is 15 - 3 - 7 = 5.
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationConsider bag (1,1)
Avg. = 3, 1 sack has more than 5 and ** ⇒ 2 conditions are being satisfied. ⇒ (can't be condition-3 ⇒ 9 coins as the total sum of coins is itself 3 * 3 = 9)
⇒ bag (1,1) has 1, 1, 7 coins with average = 3.
Consider bag (1,3)
Avg. = 5 ⇒ Sum = 15.
Median = 6 and 2 sacks have more than 5 and * ⇒ (1 condition is satisfied)
Not condition ii as the median is 6 & Not condition iii as the sum of 2 sacks itself will become 6 + 9 = 15
⇒ 1, 6, c are the coins ⇒ For sum = 15 ⇒ c = 15 - 1 - 6 = 8
⇒ bag (1,3) has 1, 6, 8 coins with average = 5.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Consider bag (3,3)
0 sacks have more than 5 coins and ** ⇒ conditions i & ii are being satisfied.
⇒ 1,1,c are the coins. Now c = 1 or 2 or 3 or 4 ⇒ c = 1 or 4 for number of coins to be a multiple of 3.
But c = 1 as no other bag has the possibility to get avg. = 1 as bag (2,2) should have 1, b, c coins and b and c should be more than 1 as only 1*
⇒ bag (3,3) has 1, 1, 1 coins with average = 1.
Now, we can fill the averages in all the bags.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

In bag (2,3) Avg. = 9 ⇒ 9, 9, 9 are the coins.
In bag (2,2) ⇒ Avg. = 2 ⇒ Sum = 6 and only 1* ⇒ smallest element should be 1.
⇒ 1, b, c are the coins where b + c = 5 and b, c can't be equal to 1 and less than 5 ⇒ 2 + 3 = 5 is the only possibility.
⇒1, 2, 3 are the coins with average = 2.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Considering bag (3,2)
Avg. = 6 ⇒ Sum = 18.
2 sacks more than 5 coins and ** ⇒ 2 sacks have 1 and 9 coins.
⇒ bag (3,2) has 1, c, 9 coins and c = 18 - 1 - 9 = 8
⇒ bag (3,2) has 1, 8, 9 coins with average = 6 coins.
==> Final required table, bracket number ⇒ average coins per sack in the bag.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Bag (1,1) ⇒ 2 sacks with 1 coins, (2,1) ⇒ 1 sack, (2,2) ⇒ 1 sack, (3,2) ⇒ 1 sack, (1,3) ⇒ 1 sack, (3,3) ⇒ 3 sacks.⇒ Total = 2 + 1 + 1 + 1 + 1 + 3 = 9 sacks.

Q5: In how many boxes do all three sacks contain different numbers of coins?

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Ans: 5
We are given that each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.
The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same.
⇒ The total number of coins in a box range from 3 (1 + 1 + 1) to 27 (9 + 9 + 9)
Since, it is given that the average number of coins per sack in the boxes are all distinct integers ⇒ The total number of coins in a box would be 3, 6, 9, 12, 15, 18, 21, 24, 27 ⇒ averages of 1, 2, 3, 4,....,9 ⇒ Sum = 45.
⇒ Sum of averages coins in a box in a row or column = 45/3 = 15 [The total number of coins in each row is the same. The total number of coins in each column is also the same.] ==> (1)
Let us represent the final configuration of the sacks in boxes as follows:
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationAlso a bag (x, y) ⇒ bag in xth row and yth column.
We are given 2 clues ⇒ Table-1 & Table-2
Consider bag (3,1)
⇒ From Table-1 ⇒ Median = 8 & From Table-2 all 3 sacks have more than 5 coins. Also * ⇒ There is a 9 in one of the sacks.
⇒ c, 8, 9 are the coins in bag (3,1), now c > 5 & c + 8 + 9 should be a multiple of 3 ⇒ c = 7 is the only possibility.
⇒ bag (3,1) has 7, 8, 9 coins with average = 8.
Consider bag (2,1)
Median = 2 and 1 sack has more than 5 coins. Also ** ⇒ conditions i & iii should be satisfied
⇒ 1, 2, 9 are the coins in bag (2,1) with average = 4
Consider bag (1,2)
Median = 9 and 2 elements are more than 5. Also * ⇒ (9 is present & 1 is not present)
⇒ c, 9, 9 are the coins in bag (1,2) and c is not equal to 1 and less than 5 ⇒ c = 3 for c + 18 to be a multiple of 3.
⇒ 3, 9, 9 are the coins in bag (1,2) with average = 7.
Capturing this info. in the table:
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationFrom (1), The average in bag (1,1) is 15 - 4 - 8 = 3.
From (1), The average in bag (1,3) is 15 - 3 - 7 = 5.
Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT PreparationConsider bag (1,1)
Avg. = 3, 1 sack has more than 5 and ** ⇒ 2 conditions are being satisfied. ⇒ (can't be condition-3 ⇒ 9 coins as the total sum of coins is itself 3 * 3 = 9)
⇒ bag (1,1) has 1, 1, 7 coins with average = 3.
Consider bag (1,3)
Avg. = 5 ⇒ Sum = 15.
Median = 6 and 2 sacks have more than 5 and * ⇒ (1 condition is satisfied)
Not condition ii as the median is 6 & Not condition iii as the sum of 2 sacks itself will become 6 + 9 = 15
⇒ 1, 6, c are the coins ⇒ For sum = 15 ⇒ c = 15 - 1 - 6 = 8
⇒ bag (1,3) has 1, 6, 8 coins with average = 5.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Consider bag (3,3)
0 sacks have more than 5 coins and ** ⇒ conditions i & ii are being satisfied.
⇒ 1,1,c are the coins. Now c = 1 or 2 or 3 or 4 ⇒ c = 1 or 4 for number of coins to be a multiple of 3.
But c = 1 as no other bag has the possibility to get avg. = 1 as bag (2,2) should have 1, b, c coins and b and c should be more than 1 as only 1*
⇒ bag (3,3) has 1, 1, 1 coins with average = 1.
Now, we can fill the averages in all the bags.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

In bag (2,3) Avg. = 9 ⇒ 9, 9, 9 are the coins.
In bag (2,2) ⇒ Avg. = 2 ⇒ Sum = 6 and only 1* ⇒ smallest element should be 1.
⇒ 1, b, c are the coins where b + c = 5 and b, c can't be equal to 1 and less than 5 ⇒ 2 + 3 = 5 is the only possibility.
⇒1, 2, 3 are the coins with average = 2.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Considering bag (3,2)
Avg. = 6 ⇒ Sum = 18.
2 sacks more than 5 coins and ** ⇒ 2 sacks have 1 and 9 coins.
⇒ bag (3,2) has 1, c, 9 coins and c = 18 - 1 - 9 = 8
⇒ bag (3,2) has 1, 8, 9 coins with average = 6 coins.
==> Final required table, bracket number ⇒ average coins per sack in the bag.

Practice Question - 74 (Quant Based) | 100 DILR Questions for CAT Preparation

Bags with different number of coins in all 3 sacks are (2,1), (3,2), (2,2), (3,2), (1,3) ⇒ 5 bags.

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FAQs on Practice Question - 74 (Quant Based) - 100 DILR Questions for CAT Preparation

1. What is the format of the Quantitative Aptitude section in the CAT exam?
Ans. The Quantitative Aptitude section in the CAT exam typically consists of multiple-choice questions (MCQs) and non-MCQs. The questions assess a candidate's mathematical skills, covering topics such as arithmetic, algebra, geometry, and data interpretation. Each question usually has a specific time limit, contributing to the overall time management strategy required during the exam.
2. How can I effectively prepare for the Quantitative Aptitude section of the CAT exam?
Ans. Effective preparation for the Quantitative Aptitude section includes several strategies: regular practice of quantitative problems, understanding key concepts, solving previous years' question papers, and taking mock tests. It is also beneficial to identify your weak areas and focus on improving them through targeted practice and revision.
3. Are there any specific topics I should focus on for the Quantitative Aptitude section?
Ans. Yes, candidates should focus on several key topics for the Quantitative Aptitude section, including Number Systems, Percentages, Profit and Loss, Ratio and Proportion, Time and Work, Time and Distance, Algebra, Geometry, and Data Interpretation. Mastery of these topics will help in tackling a wide range of questions.
4. What are some common mistakes to avoid while attempting the Quantitative Aptitude questions in the CAT exam?
Ans. Common mistakes to avoid include misreading the questions, neglecting to check for simple calculation errors, spending too much time on difficult questions, and not managing time effectively throughout the exam. It's also crucial to practice under timed conditions to simulate the exam experience.
5. How important is time management in the Quantitative Aptitude section of the CAT exam?
Ans. Time management is extremely important in the Quantitative Aptitude section of the CAT exam. With a limited amount of time to answer a significant number of questions, candidates must develop strategies to quickly identify and solve problems. Practicing with a timer and learning to prioritize questions based on difficulty can significantly enhance performance.
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