number system Model Questions & Answers, Practice Test for ssc chsl tier 1 2023

Answer: (d)

$(34^43 + 43^34)/7 = [{(35 – 1)^43 + (42 + 1)^34}/7]$.

Applying binomial theorem to (35 – 1)43, all terms will be divisible by 35 (i.e. 7) except the last term which will be –1.

Similarly, last term of $(42 + 1)^34$ will be +1.

Therefore, $34^43 + 43^34$ will leave remainder [(–1) + (+1)] = 0, when divided by 7.

Answer: (c)

Here, three–digits number = XY5

XY5 × Z = X215

So, Z can take value 1, 3, 5, 7 and 9.

But only 9 satisfies it, then X = 1, Y = 3 and Z = 9

q 135 × 9 = 1215

value of X + Y + Z = 1 + 3 + 9 = 13

Answer: (a)

Required time = L.C.M of 24, 36 and 30

= 360 seconds = 6 minutes

Answer: (a)

Suppose digit at tens place is 2x and unit place is x.

So original number = 20x + x = 21x

After interchanging the number

= 10x + 2x = 12x

21x – 12x = 27

x = 3

So, number = 63

Anuj's monthly salary = 324000 ÷ 12 = 27000

Answer: (b)

Let the total number of packages be x.

After uploading $2/5x$ packages remaining packages are

$x - 2/5x = 3/5x$

According to the question,

When he uploaded another 3 packages then of original no. of packages remained.

∴ ${3x}/5 - 3 = x/2$

$3/5x - {1x}/2 = 3$

6x – 5x = 30 ⇒ x = 30

Hence, 30 packages were in the van before the first delivery.