Which of the following statements is necessarily false?

A) D1 and D3 together sold more ACs as compared to D2 and D4 together.

B) D4 sold more Split ACs as compared to D3.

C) D2 sold the highest number of ACs.

D) D1 and D3 sold an equal number of Split ACs.

Dealer	$W_I$	$W_N$	$W_T$	$S_I$	$S_N$	$S_T$	Total
D1		$0$	$a$			$2a$
D2		$2y$	$3x$	$2b$
D3		$y$	$x$	$b$
D4		$0$	$x$	$b$
Total		$6$		$36$

We first find data that we can add to the table which is already given in the question.

Until point 3, there is no data we can directly add. Point 3 gives the total for Window Non-Invertor & Split Invertor.

$W_N = 6$

$S_I = 36$

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For D1, point 4 says that number of split sold is twice window ACs.

Let $W_T = a$, then $S_T$ would be $2a$. We can add this to our table.

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For window ACs, point 5 says D3 and D4 sold equal, let's say $x$ and D2 sold three times of that, hence $3x$

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For window non-invertor, point 6 says D2 and D3 are the only ones who sold. Let's say D3 sold $y$, then D2 sold $2y$. Since they are the only ones who sold it, we can put 0 for rest.

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For split inverter ACs, point 7 says D3 and D4 sold equal, let's say $b$ and D2 sold twice that, hence $2b$

Dealer	$W_I$	$W_N$	$W_T$	$S_I$	$S_N$	$S_T$	Total
D1		$0$	$a$			$2a$
D2		$2y$	$3x$	$2b$
D3		$y$	$x$	$b$
D4		$0$	$x$	$b$
Total		$6$		$36$

We can see that we have the total for $W_N$ and also every cell data.

So, $y + 2y = 6$

$y = 2$

We can replace the variables with numbers in our table.

Dealer	$W_I$	$W_N$	$W_T$	$S_I$	$S_N$	$S_T$	Total
D1		$0$	$a$			$2a$
D2		$4$	$3x$	$2b$
D3		$2$	$x$	$b$
D4		$0$	$x$	$b$
Total	$9$	$6$	$15$	$36$	$9$	$45$	$60$

We know that $W_I$ = 20% of invertor ACs

Hence, $S_I$ would be 80%

Given: $S_I = 36$

Hence, we can find total invertor ACs

$80$ of $I$ = $36$

$80/100 * I = 36$

$I = 45$

$I = S_I + W_I$

$45 = 36 + W_I$

Hence, $W_I = 9$

$W_T = 9 + 6$

$W_T = 15$

Also, it is given that out of the total number of ACs sold 25% were window variant

=> 25% of total = 15

=> total ACs sold = 60

Dealer	$W_I$	$W_N$	$W_T$	$S_I$	$S_N$	$S_T$	Total
D1		$0$	$a$			$2a$
D2		$4$	$3x$	$2b$
D3		$2$	$x$	$b$	$3$
D4		$0$	$x$	$b$
Total	$9$	$6$	$15$	$36$	$9$	$45$	$60$

From clue 2, we know D3 sold 5 Non-inverter ACs.

Now, $W_N$ = 2

therefore, $S_N$ = 5-2 = 3

Dealer	$W_I$	$W_N$	$W_T$	$S_I$	$S_N$	$S_T$	Total
D1	$5$	$0$	$5$			$10$
D2	$2$	$4$	$6$	$2b$
D3	$0$	$2$	$2$	$b$	$3$	$b + 3$
D4	$2$	$0$	$2$	$b$
Total	$9$	$6$	$15$	$36$	$9$	$45$	$60$

From the table, we know,

$W_T's$ total = 15

=> $a + 3x + x + x = 15$

=> $a + 5x = 15$

Also, it is given that Every dealer sold at least two window ACs. (clue 1)

Therefore, th only possibility we have is, $a = 5$ and $x =2$

Dealer	$W_I$	$W_N$	$W_T$	$S_I$	$S_N$	$S_T$	Total
D1	$5$	$0$	$5$	$8$	$2$	$10$
D2	$2$	$4$	$6$	$14$
D3	$0$	$2$	$2$	$7$	$3$	$10$
D4	$2$	$0$	$2$	$7$
Total	$9$	$6$	$15$	$36$	$9$	$45$	$60$

From clue 2,

D1 sold 13 inverter ACs

Therefore, $W_I$ + $S_I$ = 13

=> $S_I = 8$

Now, we can find the value of $b$

=> $8 + 2b + b + b = 36$

=> $b = 7$

Dealer	$W_I$	$W_N$	$W_T$	$S_I$	$S_N$	$S_T$	Total
D1	$5$	$0$	$5$	$8$	$2$	$10$
D2	$2$	$4$	$6$	$14$
D3	$0$	$2$	$2$	$7$	$3$	$10$
D4	$2$	$0$	$2$	$7$
Total	$9$	$6$	$15$	$36$	$9$	$45$	$60$

This is the final table we can make ,

though there will be some values which we won't be able to find from the clues, but remember that this is very normal in CAT DILR where you might not get a definite answer or the answer can have multiple solutions.

So, instead of giving up you should directly go on to the questions and try to answer them.

Dealer	$W_I$	$W_N$	$W_T$	$S_I$	$S_N$	$S_T$	Total
D1	$5$	$0$	$5$	$8$	$2$	$10$
D2	$2$	$4$	$6$	$14$
D3	$0$	$2$	$2$	$7$	$3$	$10$
D4	$2$	$0$	$2$	$7$
Total	$9$	$6$	$15$	$36$	$9$	$45$	$60$

We see that D1 & D3 sold $27$ ACs together which is less than $60-27=33$ sold by D2 & D4. $\Rightarrow$ Option -A is definitely false.