Question 20/20: Set 3 - Try Out - Mathematical Reasoning (SNBT)

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Toko Maju receives shipments of cooking oil from three suppliers for resale with the following schedule:

Oil	Delivery Schedule	Volume per shipment (liters)
$A$	Every $3$ days	$10$
$B$	Every $4$ days	$15$
$C$	Every $x$ days	$20$

On April $1$ , $2023$ , the shop received shipments of oil brands $A$ , $B$ , and $C$ simultaneously for the first time.

What is the number of days in April $2023$ where Toko Maju did not receive any shipments of oil $A$ or $B$ ?

Explanation

We need to find the number of days without shipments of oil $A$ or $B$ . The most efficient way is to count the days with shipments, then subtract that from the total days in April ( $30$ days).

Here is the breakdown of the delivery schedule:

Oil Type	Delivery Dates (Arithmetic Sequence)	Total Days
Oil $A$ (Every $3$ days)	$1, 4, 7, 10, 13, 16, 19, 22, 25, 28$	$10$
Oil $B$ (Every $4$ days)	$1, 5, 9, 13, 17, 21, 25, 29$	$8$
Union ( $A \cup B$ )	$1, 4, 5, 7, 9, 10, 13, 16, 17, 19, 21, 22, 25, 28, 29$	$15$

From the table above, there are $15$ days where the shop receives a shipment (either $A$ , $B$ , or both).

Thus, the number of days without shipments is:

\text{Empty Days} = \text{Total April} - \text{Delivery Days}

\text{Empty Days} = 30 - 15 = 15

So, there are $15$ days where the shop did not receive any shipment of oil $A$ or $B$ .

Command Palette

Number 20

Explanation