Tom now had access to the ammunition [ammo]. He now had to load a correct amount of ammo to shoot the combatant. The gun calculated the amount of ammo to be loaded and displayed the following to Tom –

“There are 27 bullets that can be fired in each roundand 64 rounds are available, which means $27 \times 64 = 2^{x} \times 3^{y}$ bullets can be shot”

The gun can be activated digitally by entering another passcode, which is the numerical value of (x-y).

What is the passcode that Tom has to enter? ____ [Enter a numerical value]

_

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Solution

We know that $27 = 3^{3}$
Also $64 = 8^{2} = {(2^{3})}^{2} = 2^{(3 \times 2)} = 2^{6}$
Now, $27 \times 64 = 3^{3} \times 2^{6}$

Comparing it with $2^{x} \times 3^{y}$ , we get $x = 6$ and $y = 3$

x-y = 6-3 =3

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Similar questions

Having entered the passcode correctly, Tom got his mission. He needs to fight an enemy combatant and get information about the next clue. Tom found the room where the combatant was, but to enter the room, he needed another passcode.The passcode is the answer to the following display:

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___

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___

With sufficient ammo loaded, Tom managed to overpower his combatant and got the next clue and exited The Architecture.

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___

Once Tom answered the question to unlock the car, he hopped in and drove off to reach his destination – a building calledTheArchitecture.This building closelyresembles a Rubik’s Cube, in the sense that the “rooms” of The Architectureare like the “cubes” of the Rubik’s Cube, as shown:

This building has 3 floors and each floor has 3 $\times$ 3 [read 3 by 3 – which means there are 3 rows and 3 columns] rooms which are all identical in size and shape.Tom stopped the car in front of the building.To enter this architecture, he should enterapasscodewhich is equal to the total number of rooms [cubes] in the building.

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___

Having unlocked the door, Tom proceeded to battle with his combatant. Tom realized that he would need some ammunition [bullets] to counter his opponent. He found a chest full of ammunition which had a display on it. It had four buttons on it, A, B, C and D and on each button, there were some laws [equations which are always true]. The chest would open only if Tom pressed ALL the buttons with a correct law on it.

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We know that 27=33 Also 64=82=(23)2=2(3×2)=26 Now, 27×64=33×26 Comparing it with 2x×3y, we get x=6 and y=3 x-y = 6-3 =3

We know that $27 = 3^{3}$
Also $64 = 8^{2} = {(2^{3})}^{2} = 2^{(3 \times 2)} = 2^{6}$
Now, $27 \times 64 = 3^{3} \times 2^{6}$

Comparing it with $2^{x} \times 3^{y}$ , we get $x = 6$ and $y = 3$

x-y = 6-3 =3