Logical Reasoning

Arrangements

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Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individually interviews each of the candidates individually and awards a token only if she recommends funding. A token has a face value of 2, 3, 5, 7, 11, or 13. Each interviewer awards tokens of a single face value only.

Once all six interviews are over for a candidate, the candidate receives a funding that is Rs.1000 times the product of the face values of all the tokens. For example, if a candidate has tokens with face values 2, 5, and 7, then they get a funding of Rs.1000 × (2 × 5 × 7) = Rs.70,000.

Pragnyaa, Qahira, Rasheeda, Smera, and Tantra were five candidates who received funding. The funds they received, in descending order, were Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000.

The following additional facts are known:

Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.

Rasheeda received the highest number of tokens that anyone received, but she did not receive one from Esther.

Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.

Who among the following definitely received a token from Bithi but not from Dhanavi

Rasheeda

Pragnyaa

Tantra

Qahira

✅ Correct Option: 2

Slide 1/10

Understanding the set :-

There are 5 interviewers - Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima

there are 5 candidates - Pragnyaa, Qahira, Rasheeda, Smera, and Tantra

Every interviewer individually interviews each of the candidates individually and awards a token

A token has a face value of 2, 3, 5, 7, 11, or 13. Each interviewer awards tokens of a single face value only

When all six interviews are over for a candidate, the candidate receives a funding that is Rs.1000 times the product of the face values of all the tokens (i.e., if a candidate has tokens with face values 2, 5, and 7, then they get a funding of Rs.1000 × (2 × 5 × 7) = Rs.70,000.)

Total funding to all the 5 candidates - $Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000$ in any order

In this set we will form a table where we will find the token value with each interviewer and the total funding each candidate will receive.

Candidates	Funds (in 1000s)	(2)	(3)	(5)	(7)	(11)	(13)
	390
	210
	165
	77
	66

In this table we will fill the name candidate who have received the funding given in column 2.

And in the first row with token number we are required to find the interviewer who has particular token.

Also, in the other rows and column we will find the token numbers given to have that particular funding.

We know, funding is given through multiplying Rs.1000 with the product of the face values of all the tokens.

Funds	(2)	(3)	(5)	(7)	(11)	(13)
390	√	√	√	X	X	√
210	√	√	√	√	X	X
165	X	√	√	X	√	X
77	X	X	X	√	√	X
66	√	√	X	X	√	X

From the funding values we can deduce that -

For 66 to be the funding value - we will need a token of 11 ; after which we are left with 6 from the given token values 2 *3 = 6

=> $66 = 2 * 3* 11$

For 77 to be the funding - only possibility = 7 * 11

=> $77 = 7 * 11$

for 165 to be the funding value - we will surely need a 5 and a 11 - now we are only left with 3

=> $165 = 3 * 5 * 11$

For 210 to be the funding value - we will need a 5, 2 to make it 10 - now we are left with 21 = 7 * 3

=> $210 = 2 * 3* 5* 7$

Lastly for 390 to be the funding - we will again need a 5 and a 2 to make it 10 - now we are left with 39 = 13 * 3

=> $390 = 2 * 3 * 5 * 13$

Candidates	Funds	(2)	Fathima(3)	(5)	(7)	(11)	(13)
	390	√	√	√	X	X	√
	210	√	√	√	√	X	X
	165	X	√	√	X	√	X
Qahira	77	X	X	X	√	√	X
	66	√	√	X	X	√	X

Now from clue 1 ,

Fathima awarded tokens to everyone except Qahira

From the table we can see that only token 3 was given to everyone except one person,

Therefore, we can conclude that Fathima had token 3.

Also, Since she has only not given token to Qahira therefore we can says that Funding of $rs 77000$ was given to Qahira.

Candidates	Funds	(2)	Fathima(3)	(5)	(7)	(11)	Adhara (13)
Pragnyaa	390	√	√	√	X	X	√
	210	√	√	√	√	X	X
	165	X	√	√	X	√	X
Qahira	77	X	X	X	√	√	X
	66	√	√	X	X	√	X

Continuing with clue 1,

Adhara awarded tokens to no one except Pragnyaa.

From the table we can see that token 13 was given to only one person

Therefore, Adhara had token 13

and Pragnyaa had received a funding of $Rs 390000$ .

Candidates	Funds	(2)	Fathima(3)	(5)	(7)	(11)	Adhara (13)
Pragnyaa	390	√	√	√	X	X	√
Rashida	210	√	√	√	√	X	X
	165	X	√	√	X	√	X
Qahira	77	X	X	X	√	√	X
	66	√	√	X	X	√	X

Using clue 2 ,

Rashida received the highest number of tokens

So, there are two candidates receiving the highest number of tokens

which is, 4 token received by - funding of $Rs 390000$ and $Rs 210000$

But $Rs 390000$ we know is received by Pragnyaa

Therefore, Rashida received funding of $Rs 210000$

Candidates	Funds	(2)	Fathima(3)	(5)	(7)	Esther (11)	Adhara (13)
Pragnyaa	390	√	√	√	X	X	√
Rashida	210	√	√	√	√	X	X
	165	X	√	√	X	√	X
Qahira	77	X	X	X	√	√	X
	66	√	√	X	X	√	X

Continuing for clue 2,

Rashida received the highest number of tokens that anyone received, but she did not receive one from Esther.

=> we know, Rashida had not received token from two of the interviewers who had token value of 11 and 13.

And, Adhara has token value of 13

Therefore, Ester had token value of 11.

Candidates	Funds	(2)	Fathima(3)	(5)	(7)	Esther (11)	Adhara (13)
Pragnyaa	390	√	√	√	X	X	√
Rashida	210	√	√	√	√	X	X
	165	X	√	√	X	√	X
Qahira	77	X	X	X	√	√	X
	66	√	√	X	X	√	X

Using clue 3,

Bithi awarded a token to Smera but not to Qahira

We know, Qahira haven't got token number 2, 3, 5, and 13

Out of which , token 3 is with Fathima

and token 13 with Adhara

Therefore, Bithi will have one of token 2 or 5

If, Bithi has token value 2

=> Smera will be with funding $Rs 66,000$

(As Bithi awarded token to smera)

If, Bithi has token value 5

=> Smera will be with funding $Rs 1,65,000$

Candidates	Funds	Bithi/ Chhaya (2)	Fathima(3)	Bithi/ Chhaya (5)	Dhanavi (7)	Esther (11)	Adhara (13)
Pragnyaa	390	√	√	√	X	X	√
Rashida	210	√	√	√	√	X	X
Smera/Tantra	165	X	√	√	X	√	X
Qahira	77	X	X	X	√	√	X
Smera/Tantra	66	√	√	X	X	√	X

Continuing with clue 3,

Dhanavi awarded a token to Qahira but not to Smera.

There are only two interviewer giving token to Qahira (token - 7 & 11)

Of which, token value -11, is with Esther.

=> Dhanavi will have token value of 7.

Also, Dhanavi had not given token to Smera.

But, Dhanavi has not given token to either of funding, $Rs 165000$ or $Rs 66,000$

Therefore, funding of $Rs 165000$ or $Rs 66,000$ will be of either Smera or Tantra, which we can't determine.

Therefore, we can't determine token value of Bithi or Chhaya, which will be one among 2 or 5.

Candidates	Funds	Bithi/ Chhaya (2)	Fathima(3)	Bithi/ Chhaya (5)	Dhanavi (7)	Esther (11)	Adhara (13)
Pragnyaa	390	√	√	√	X	X	√
Rashida	210	√	√	√	√	X	X
Smera/Tantra	165	X	√	√	X	√	X
Qahira	77	X	X	X	√	√	X
Smera/Tantra	66	√	√	X	X	√	X

As observed above Pragnyaa received a token from Bithi but not from Dhanvi : Option 2

Question 6

How many tokens did Qahira receive?

Question 8

How many tokens did Chhaya award?

Question 9

How many tokens did Smera receive?

Question 10

Which of the following could be the amount of funding that Tantra received?

(a) Rs. $66,000$

(b) Rs. $165,000$

Funds	(2)	(3)	(5)	(7)	(11)	(13)
390	√	√	√	X	X	√
210	√	√	√	√	X	X
165	X	√	√	X	√	X
77	X	X	X	√	√	X
66	√	√	X	X	√	X

Funds	(2)	(3)	(5)	(7)	(11)	(13)
390	√	√	√	X	X	√
210	√	√	√	√	X	X
165	X	√	√	X	√	X
77	X	X	X	√	√	X
66	√	√	X	X	√	X

Who among the following definitely received a token from Bithi but not from Dhanavi

Solution

More from this set:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)

Funds	(2)	(3)	(5)	(7)	(11)	(13)
390	√	√	√	X	X	√
210	√	√	√	√	X	X
165	X	√	√	X	√	X
77	X	X	X	√	√	X
66	√	√	X	X	√	X