Numerics (Calculator Req.) - Italian MCQ

This numerical reasoning question has two important lessons: taking out the common factor and using the multiple-choice answers to your advantage.

To solve this problem, take out the common factor in the numerator and in the denominator in order to simplify the expression.

The result is:

. You know that

, thus

.

Multiply both sides by 2y and get 5=2y, which is reducible to y=2.5.

While this is a straightforward solution, taking a glance at the possible answers before solving can expedite the process even further. After taking out the common factor, a sharp eye could have noticed that the ratio between the numerator and the denominator is 2.5:y. This is easier to notice if you already know that 2.5 is one of the answers. Looking at the answers can be a helpful tool during numerical reasoning tests

Geometry problems can often seem daunting at first, only because the solver is unaware of a certain basic rule that would clear it all up. In this case, you must realize that a parallelogram is simply a rectangle whose corner has been displaced. If you imagine cutting the polygon in the picture along the dashed line and moving the triangle to the right side, such that d and b are coinciding sides, you get a perfect rectangle.

We know the area of a rectangle is the product of the base and height, so parallelograms will work the same way: the area of a parallelogram equals the product of the length of the base and the corresponding height (i.e. the height that is perpendicular to the chosen base).

Substituting with the numbers from the question: 8 x 5 = 40.

Therefore, the area of the parallelogram is 40 cm².

Alcohols are organic compounds that contain the hydroxyl group (-OH) as their functional group. The hydroxyl group is characterized by the presence of an oxygen atom bonded to a hydrogen atom. This functional group gives alcohols their characteristic properties, such as the ability to undergo reactions like dehydration and esterification.

Given:

Watermelon costs = Rs. 25 per fruit

Mango costs =  Rs. 20 per fruit

An apple costs = Rs. 15 per fruit

Orange costs = Rs. 10 per fruit

If Indu bought 2 watermelons, 5 mangoes, 3 apples, and some oranges and paid a bill of Rs 285.

Let, Indu buy x orange.

$\begin{array}{rl}& \therefore 2\times 25+5\times 20+3\times 15+x\times 10=285\\ & \Rightarrow 50+100+45+10x=285\\ & \Rightarrow 10x=285-195\\ & \Rightarrow 10x=90\end{array}$

$\Rightarrow x=\text{Rs}\text{. }9$ per fruit

Hence, the correct answer is "9".

Given:

45% × X = 60$\frac{6}{10}$

Calculation:

According to the question,

45% × X = 60$\frac{6}{10}$

⇒ 45/100 × X = 606/10

⇒ X = 6060/45 

⇒ X = 134.67

∴ The correct answer is  134.67

Given:

500

Formula:

Number of total divisors = ((a+1)(b+1)) where (a) and (b) are the exponents of the prime factors.
For proper divisors: Subtract 1 to exclude the number itself.

Solution:

Factor = $(500=2^2\times 5^3)$

((2+1)(3+1) - 1 = 11).

Explanation:

Ratio of their daily wages = 5 : 6 : 4

Total wage = Rs. 1800

6 × 5x + 4 × 6x + 4 × 9x = 1800 [As A, B, C works for 6, 4, 9 days respectively]

Or, 90x = 1800

$x=\frac{1800}{90}$

Total amount of A = $\frac{1800\times 30}{90}$

 = Rs. 600

Explanation:

Given:

$\frac{1}{2+\frac{1}{3+\frac{1}{4+\frac{1}{5}}}}$

$=\frac{1}{2+\frac{1}{3+\frac{1}{\frac{21}{5}}}}$

$=\frac{1}{2+\frac{1}{3+\frac{5}{21}}}$

$=\frac{1}{2+\frac{1}{\frac{68}{21}}}$

$=\frac{1}{2+\frac{21}{68}}$

$=\frac{1}{\frac{157}{68}}$

$=\frac{68}{157}$

Explanation:

Let C.P. be Rs. $x$.

Then, 

$\frac{1920-x}{x}\times 100=\frac{x-1280}{x}\times 100$

$\Rightarrow 1920-x=x-1280$

$\Rightarrow 2x=3200$

$\Rightarrow x=1600$

$\therefore$ Required S.P. $=125\mathrm{\%}$ of Rs. $1600$

$=$ Rs. $(\frac{125}{100}\times 1600)$

= Rs. 2000

Explanation:

Speed $=S=\frac{D}{T}$

Average Speed $=\frac{\text{ Total distance travelled }}{\text{ Total time taken }}$

Total distance $=96+124+105=325km$

Total Time $=t1+t2+t3$

$=\frac{d1}{s1}+\frac{d2}{s2}+\frac{d3}{s3}$

$=\frac{96}{16}+\frac{124}{31}+\frac{105}{7}$

$=25$ hours

$\therefore$ Average speed $=\frac{325}{25}$

= 13 km/hr

Explanation:

R cycles $\frac{1}{3}$rd as fast as Q.

$\therefore$ Speed of R = $\frac{1}{3}$rd of Speed of Q.

$\therefore$ R takes 3 times more time than Q.

R needs 45 minutes to finish the race so Q takes $\frac{45}{3}=15$ minutes to finish the race.

P is twice as fast as Q.

So, P takes half the time as Q =$\frac{15}{2}=7.5$ minutes.

 This means that when P reaches the finish line, Q is only half way.

So, Q is at half distance from finish line i.e., $\frac{4500}{2}$

= 2250 m

Explanation:

Let income of A and B be 3x and 2x respectively. 

Also, their expenditure is 5y and 3y.

Now, according to question,

3x - 5y = 1000 ------- (i) × 3

2x - 3y = 1000 ---------- (ii) × 5

9x - 15y - 10x + 15y = 3000 - 5000

Or, -x = -2000

x = 2000

Then, 

Income of A = 3x 

= 3 × 2000 

= Rs. 6000

Explanation:

LCM of 36, 42 and 72,

36 = 2 × 2 × 3 × 3

42 = 2 × 3 × 7

72 = 2 × 2 × 2 × 3 × 3

LCM = 2 ×2 × 2 × 3 × 3 × 7 = 504 seconds.

LCM of 36, 42 and 72 is 504

So, the lights will change simultaneously after 8 minutes and 24 seconds.

Explanation:

Let S be the sample space.

Then,

$n(S)={}^{52}{C}_2=\frac{(52\times 51)}{(2\times 1)}=1326$

Let E = event of getting 2 kings out of 4.

$\therefore n(E)={}^4{C}_2=\frac{(4\times 3)}{(2\times 1)}=6$

$\therefore P(E)=\frac{n(E)}{n(S)}=\frac{6}{1326}$

$=\frac{1}{221}$

Explanation:

Vimal's 1 day work $=\frac{1}{20}$

Since, Vimal and Kamal can together complete in 12 days.

i.e. (Vimal + Kamal)'s 1 day work $=\frac{1}{12}$

Then,

Kamal's 1 day work,

$=\frac{1}{12}-\frac{1}{20}$

$\Rightarrow \frac{2}{60}$ 

$\Rightarrow \frac{1}{30}$

If Kamal Works only for half a day daily, then his 1 day work becomes $\frac{1}{2}\times \frac{1}{30}=\frac{1}{60}$

Therefore, 1 day work of both Vimal and Kamal,

$=\frac{1}{20}+\frac{1}{60}$ 

$\Rightarrow \frac{4}{60}$ 

$\Rightarrow \frac{1}{15}$

So, the work will be completed in 15 days.

Explanation:

The possible cases can be:

1. 4 boys and 4 girls
2. 3 boys and 3 girls
3. 2 boys and 2 girls

Ways of selecting of 4 boys out of $4={}^4{C}_4=1$

Ways of selecting of 3 boys out of $4={}^4{C}_3=4$

Ways of selecting of 2 boys out of $4={}^4{C}_2=6$

Ways of selecting of 4 girls out of $6={}^6{C}_4=15$

Ways of selecting of 3 girls out of $6={}^6{C}_3=20$

Ways of selecting of 2 girls out of $6={}^6{C}_2=15$

$\therefore$ Total possible ways $N=(1\times 15)+(4\times 20)+(6\times 15)$

$N=15+80+90=185$

Explanation:

Let P, Q and R represent their respective monthly incomes. 

Then, we have:

P + Q = (5050 x 2) = 10100 .... (i)

Q + R = (6250 x 2) = 12500 .... (ii)

P + R = (5200 x 2) = 10400 .... (iii)

Adding (i), (ii) and (iii), we get:  

2(P + Q + R) = 33000  or   P + Q + R = 16500 .... (iv)

Subtracting (ii) from (iv), we get 

P = 4000.

$\therefore$ P's monthly income = Rs. 4000.

Explanation:

Cost Price of 1 toy = Rs. $\left(\frac{375}{12}\right)$

= Rs. 31.25

Selling Price of 1 toy = Rs. 33

So, Gain = Rs. (33 - 31.25) 

= Rs. 1.75

$\therefore$ Profit $\mathrm{\%}=(\frac{1.75}{31.25}\times 100)\mathrm{\%}$

$=\frac{28}{5}\mathrm{\%}$

= 5.6%

Explanation:

Let the side of cube = 10 cm

∴ Original volume = 10 × 10 × 10 = 1000 cm³

Now, side of new cube: 

= 10 - 25% of 10 = 7.5

∴ New volume = 7.5 × 7.5 × 7.5 = 421.875 cm³

∴ Required ratio:

$=\frac{1000}{421.875}$

$=\frac{1000000}{421875}$

$=\frac{64}{27}$

$=64:27$

Explanation:

$BO=\mathrm{OC}=15cm$

$OD=9cm$

$BD=\sqrt{{15}^2-9^2}$

$=\sqrt{24\times 6}$

$=12cm$

$BC=2\times 12$

= 24 cm

Explanation:

External radius = 3 cm

Internal radius = (3 - 0.5) cm 

= 2.5 cm

Volume of the metal:

$=[\frac{4}{3}\times \frac{22}{7}\times \{(3{)}^3-(2.5{)}^3\}]{cm}^3$

$=(\frac{4}{3}\times \frac{22}{7}\times \frac{91}{8}){cm}^3$

$=\left(\frac{143}{3}\right){\mathrm{cm}}^3$

$=47\frac{2}{3}{cm}^3$