lcm and hcf Model Questions & Answers, Practice Test for ssc mts paper 1 2023

Answer: (e)

Suppose the original fraction is . $x/y$

According to question,

${x+x×400/100}/{y+y×500/100}=20/27⇒{x+4x}/{y+5y}=20/27$

⇒${5x}/{6y}=20/27$⇒$x/y={20×6}/{27×5}$⇒$x/y=8/9$

Answer: (a)

LCM=$ {LCM of 1,5,2,4}/{HCF of 3,6,9,27}=20/3$

Answer: (c)

The required numbers should be multiples of 144. We have the greatest number of 4 digits = 9999. On dividing 9999 by 144, we get 63 as the remainder.

∴ required greatest number of 4 digits = 9999 – 63 = 9936

Again, we have the least number of 5 digits = 10000

On dividing 10,000 by 144, we get 64 as the remainder.

∴ the required least number of 5 digits

= 10,000 + (144 – 64) = 10,080

Answer: (c)

72 – 52 = 20, 80 – 60 = 20, 88 – 68 = 20. We see that in each case, the remainder is less than the divisor by 20. The LCM of 72, 80 and 88 = 7920, therefore, the required number 7920 – 20 = 7900

Answer: (d)

Suppose original fraction is . $x/y$

∴${x+{200x}/100}/{y+{350y}/100}$=$5/12$⇒${300x}/100×100/{450y}=5/12$

⇒${300x}/{450y}=5/12$⇒${2x}/{3y}=5/12$⇒$x/y=5/12×3/2$⇒$x/y=5/8$

Short cut

${x+2x}/{y+3.5y}=5/12$

${3x}/{4.5y}=5/12$ or $x/y={5×45}/{3×12}=5/8$