Study Guide SBI PO Preliminary Examination 2019

Quantity I:

$$\begin{gathered} x^2+x-6=0 \\ {x}^2+3x-2x-6=0 \\ x(x+3)-2(x+3)=0 \\ (x-2)(x+3)=0 \\ x=2,-3 \end{gathered}$$

Quantity II:

$$\begin{gathered} y^2+7y+12=0 \\ {y}^2+4y+3y+12=0 \\ y(y+4)+3(y+4)=0 \\ (y+3)(y+4)=0 \\ y=-3,-4 \end{gathered}$$

$$\begin{gathered} x=2, y=-3 \Rightarrow x>y \\ x=-3, y=-3 \Rightarrow x=y \\ x=2, y=-4 \Rightarrow x>y \\ x=-3, y=-4 \Rightarrow x>y \\ \therefore x\ge y \end{gathered}$$

Hence, 

Quantity I$\ge$ Quantity II

A's efficiency is $25\%$ more than that of B. This means A's efficiency is $125\%$ of B's efficiency.

$\frac{125}{100}=\frac{5}{4}$

Let us assume that A does $5$ units of work daily.

So, B will do $4$ units of work daily.

Let us assume that the total work is $60$ units.

Quantity I:

A does $\frac{5}{6}$th of the work in $x$ days.

So, A will complete $(\frac{5}{6}\times 60)=50$ units of work in $x$ days.

So, $x$$=$$\frac{50}{5}=10$ days.

Quantity II:

B does $\frac{4}{5}$th of the work in $y$ days.

So, B will complete $(\frac{4}{5}\times 60)=48$ units of work in $y$ days.

So, $y=\frac{48}{4}=12$ days.

Thus, $x<y$.

Hence, Quantity I < Quantity II.

Let the eight consecutive even numbers be $x, (x+2), (x+4), (x+6), (x+8), (x+10), (x+12)$ and $(x+14)$.

Quantity I:

$(x+2)+(x+14)= 2x+16$

Quantity II:

$(x+4)+(x+10)=2x+14$

Clearly, it can be concluded that Quantity I > Quantity II.

Let market price, selling price and discount percentage of the article be $MP$, $SP$ and $d\%$, respectively.

$SP=\frac{(100-d\%)}{100}\times MP$

So,

$$\begin{gathered} MP=\frac{SP\times 100}{(100-d\%)} \\ MP=\frac{1500\times 100}{(100-12.5)} \\ MP=\frac{150000}{87.5} \end{gathered}$$

$MP=$ Rs. $1714.29$

So, 

Quantity I: Rs. $550$.

Quantity II: Rs. $1714.29$.

Hence, Quantity I < Quantity II.

Let speed of the current be $y km/hr$.

So, speed of the boat will be $(y+5y)=6y km/hr$.

So, downstream speed will be $=(6y+y)=7y km/hr$.

As per the question,

$$\begin{gathered} \frac{63}{3}=\left(7y\right) \\ 21=7y \\ y=3 \end{gathered}$$

Hence, speed of the current and the boat will be $3 km/hr$ and $18 km/hr$, respectively.

So, upstream speed will be $=x =(18-3)=15 km/hr$.

Hence, Quantity I = Quantity II.

Let the initial quantity of milk be $3x$ L, and the initial quantity of water be $x$ L.

Given, $24$ L of mixture is taken out.

Quantity of milk taken out

$=(24\times \frac{3}{4})= 18$ L

Quantity of water taken out

$=(24-18)=6$ L

The quantity of milk remaining is $(3x-18)$ L.

After $24$ L of water is added, the quantity of water remaining is $(x-6+24) =(x+18)$ L

Hence,

$$\begin{gathered} \frac{3x-18}{x+18}=\frac{2}{1} \\ 3x-18=4x+36 \end{gathered}$$

$x=54$ L

So, the total quantity of the initial mixture is

$=\left(4x\right)=(4\times 54)=216$ L

Let the speed pf Boat and the speed of Current is $x Km/Hr \& y Km/Hr$ respectively.

Upstream speed will be $=(x-y) Km/Hr$

Downstream speed will be $(x+y) Km/Hr$

As per Question,

$T=\frac{D}{x+y}$

And,

$\frac{T}{2}=\frac{D-56}{x+y}$

Now, we have,

$$\begin{gathered} \frac{D}{x+y}=\frac{2(D-56)}{x-y} \\ \frac{D}{x+y}=\frac{2D-112}{x-y} \\ \frac{(x-y)}{(x+y)}=\frac{2D-112}{D} \\ So, \\ \frac{3}{5}=\frac{2D-112}{D} (As \frac{x-y}{x+y}=\frac{3}{5}) \\ 3D=10D-560 \\ 7D=560 \\ D=\frac{560}{7}=80 Km. \\ So, \\ (x-y) = \frac{D-32}{4}=\frac{80-32}{4}=\frac{48}{4}=12 Km/Hr \\ As, \\ \frac{x-y}{x+y}=\frac{3}{5} \\ \frac{12}{x+y}=\frac{3}{5} \\ \frac{12}{12+y+y}=\frac{3}{5} (x-y=12 , x=12+y) \\ \frac{12}{12+2y}=\frac{3}{5} \\ 60=36+6y \\ 6y=24 \\ y=\frac{24}{6}=4 Km/Hr. \end{gathered}$$

 

We know that,

$$\begin{gathered} SI=\frac{P\times R\times T}{100} \\ SI=\frac{4200\times 12\times 2}{100}=1008 \end{gathered}$$

And,

$$\begin{gathered} CI=P\left[\right(1+\frac{R}{100}{)}^t-1] \\ CI =(4200-P\left)\right[(1+\frac{10}{100}{)}^2-1] \\ =(4200-P)\left[\right(\frac{100+10}{100}{)}^2-1] \\ =(4200-P\left)\right[(\frac{110}{100}{)}^2-1] \\ =(4200-P)[\frac{121}{100}-1] \\ =(4200-P)\left(\frac{121-100}{100}\right) \\ =(4200-P)\times \frac{21}{100} \\ =882-\frac{21P}{100} \end{gathered}$$

Given,

$SI-CI =294$

$$\begin{gathered} 1008-(882-\frac{21P}{100})=294 \\ 1008-882+\frac{21P}{100}=294 \\ \frac{21P}{100}=294-126 \\ P=\frac{168\times 100}{21} \end{gathered}$$

$P=$ Rs. $800$

Let the price of article B be Rs. $x$.

Then, the price of article A will be Rs. $(x-140)$.

As per the question,

$$\begin{gathered} P_A+P_B=18 \\ [40\% \times (x-140\left)\right]+[-20\% \times x] =18 \\ \frac{40}{100}\times (x-140) -\frac{20}{100}\times x = 18 \\ \frac{2}{5}(x-140) - \frac{1}{5}x=18 \\ \frac{2x}{5}-56-\frac{x}{5}=18 \\ \frac{(2x-x)}{5}=18+56 \\ \frac{x}{5}=74 \\ x=(74\times 5) \end{gathered}$$

$x=$ Rs. $370$

Let the present ages of A, B and C be $A$, $B$ and $C$ respectively.

Given,

$$\begin{gathered} B+18=A \\ B=A-18 \end{gathered}$$

And,

$A=2C$

Also,

$$\begin{gathered} \frac{B+6}{C}=\frac{3}{2} \\ \frac{A-18+6}{C}=\frac{3}{2} \\ \frac{A-12}{C}=\frac{3}{2} \\ \frac{2C-12}{C}=\frac{3}{2} \\ 4C-24=3C \end{gathered}$$

$C=24$ years

$A=(2\times 24)=48$ years

$B=48-18=30$ years

Hence, B's age four years ago

$=(30-4) = 26$ years

Let the numbers be $x, (x+2), (x+4), (x+6), (x+8)$ and $(x+10)$.

As we know, the average of three consecutive odd numbers is always the middle number.

So, the average of the first three consecutive odd numbers will be $(x+2)$.

Square of this average will be

$=(x+2{)}^2=(x^2+4x+4)$

Similarly, the average of the last three consecutive odd numbers will be $(x+8)$.

Square of this average will be

$=(x+8{)}^2=x^2+16x+64$

As per the question,

$$\begin{gathered} (x^2+16x+64)-(x^2+4x+4)=288 \\ (x^2+16x+64-x^2-4x-4)=288 \\ (12x+60)=288 \\ 12x=288-60 \\ x=\frac{228}{12}=19 \end{gathered}$$

So, the largest number will be

$=(x+10)=(19+10)=29$

As per the question,

Number of red balls $=6$

Number of green balls $=9$

Total number of balls $=15$

Probability that at least one ball is red

$=1-$ Probability that no ball is red

$=1-$ Probability that both balls are green

$$\begin{gathered} =1-\frac{{}^{9}C_2}{{}^{15}C_2} \\ =1-\frac{{\displaystyle \frac{9!}{7! 2!}}}{{\displaystyle \frac{15!}{13! 2!}}} \\ =1-\frac{9\times 8}{15\times 14} \\ =1-\frac{72}{210} \\ =1-\frac{12}{35} \\ =\frac{23}{35} \end{gathered}$$

A is thrice as efficient as B. So, A takes one-third the time that B takes to complete the work.

Let the number of days taken by A and B to complete the work be $x$ and $3x$ days, respectively.

One day work of A and B will be $\frac{1}{x}$ and $\frac{1}{3x}$ units, respectively.

As per the question,

$$\begin{gathered} (4\times \frac{1}{x}) + (15\times \frac{1}{3x}) = \frac{75}{100} \\ (\frac{4}{x}+\frac{15}{3x}) =\frac{75}{100} \\ (\frac{4}{x}+\frac{5}{x}) =\frac{3}{4} \\ \frac{9}{x}=\frac{3}{4} \\ x=\frac{9\times 4}{3}= 12 \end{gathered}$$

So, the time taken by B to complete the work alone will be

$= 3x = 3\times 12 = 36$ days

As per the question,

$r = 20\%$

$t = 2$ years

Hence, the compound interest (CI) will be

$$\begin{gathered} =P\left[\right(1-\frac{r}{100}{)}^t-1] \\ =P[(1+\frac{20}{100}{)}^2-1] \\ =P\left[\right(1+\frac{1}{5}{)}^2-1] \\ =P[(\frac{6}{5}{)}^2-1] \\ =P[\frac{36}{25}-1] \\ =P\left[\frac{36-25}{25}\right] \\ =P\left(\frac{11}{25}\right) \\ =\frac{11P}{25} \end{gathered}$$

Now, this CI is lent at $7.5\%$ on SI for $2$ years.

So, the simple interest (SI) will be

$$\begin{gathered} =\frac{{\displaystyle \frac{11P}{25}\times 7.5\times 2}}{100} \\ =\frac{11P\times 7.5\times 2}{25\times 100} \\ =\frac{165P}{2500} \end{gathered}$$

As per the question,

$$\begin{gathered} (\frac{11P}{25}+\frac{165P}{2500})=3036 \\ \left(\frac{1100P+165P}{2500}\right)=3036 \\ 1265P=(3036\times 2500) \\ P=\frac{3036\times 2500}{1265} \end{gathered}$$

$P=$ Rs. $6000$

As per the question,

Amounts are invested by A, B and C for $12$, $8$ and $6$ months, respectively.

Hence, the ratio of their share of profits will be:

$$\begin{gathered} A:B:C \\ =(25000\times 12) : (15000\times 8) : (20000\times 6) \\ =(25\times 12) : (15\times 8) : (20\times 6) \\ =5 : 2 : 2 \end{gathered}$$

Hence, A's profit will be

$=\frac{5}{(5+2+2)}\times$ Total Profit

So, Total Profit (in Rs.) $=\frac{7750\times 9}{5}=13950$

The quantity of the initial mixture is $140$ L.

After $20$ L of this mixture is given to a customer, the quantity of mixture remaining would be

$=140-20=120$ L

Hence, the quantity of water remaining is
$=30\%\times 120=\frac{30}{100}\times 120=36$ L

And, the quantity of milk remaining will be

$=120-36=84$ L

Let $x$ L of milk and $x$ L of water be added to the mixture.

$$\begin{gathered} \frac{84+x}{36+x}=\frac{2}{1} \\ 84+x=72+2x \\ x=12 \end{gathered}$$

So, the quantity of milk added is $12$ L.

Let the speed of the boat and the stream be $7x$ km/hr and $x$ km/hr, respectively.

Upstream speed will be  $=(7x-x)=6x$ km/hr.

Downstream speed will be $=(7x+x)=8x$ km/hr.

So,

$$\begin{gathered} 6x= \frac{4.2}{{\displaystyle \frac{14}{60}}} \\ 6x=\frac{42\times 60}{10\times 14} \\ 6x=18 \end{gathered}$$

$x=\frac{18}{6}=3$ km/hr

Hence, the time taken to cover the given distance downstream will be

$=\frac{17.6}{8x}=\frac{17.6}{8\times 3}=\frac{11}{15}$ hr

$=(\frac{11}{15}\times 60)=44$ min

A invests Rs. $1500$ for $12$ months.

Let the amounts invested (in Rs.) by B and C be $x$ and $y$, respectively. These amounts have been invested for $6$ and $4$ months respectively.

The profits are shared in the ratio of the products of the amounts invested and the durations of investments.

Therefore,

$$\begin{gathered} A:B:C=5:3:3 \\ (1500\times 12) : (x\times 6) : (y\times 4)=5:3:3 \\ \left(18000\right) : \left(6x\right) : \left(4y\right)=5:3:3 \\ \frac{18000}{6x}=\frac{5}{3} \\ x=\frac{18000\times 3}{5\times 6}=1800 \\ \frac{18000}{4y}=\frac{5}{3} \\ y=\frac{18000\times 3}{5\times 4}=2700 \end{gathered}$$

So, the required amount (in Rs.) is $=x+y=1800+2700=4500$.

Let the side of the square be $x$ m.

So,

$A=x^2$

$x=\sqrt{A}=\sqrt{576}=24$ m

So, length of the rectangle will be $=(x+4)=(24+4)=28$ m

Breadth of the rectangle will be $=(x-4)=(24-4)=20$ m

Hence, area of rectangle will be

$=l\times b=(28\times 20) =560$ sq. m

Let the CP (in Rs.) of A be $100x$.

So, CP (in Rs.) of B will be $=(\frac{120}{100}\times 100x)=120x$

CP (in Rs.) of C will be $=(\frac{110}{100}\times 120x)=132x$

CP (in Rs.) of D will be

$$\begin{gathered} =132x+(\frac{16}{100}\times 100x) \\ =132x+16x \\ =148x \end{gathered}$$

As per the statement given in the question,

$$\begin{gathered} 148x-100x=500 \\ 48x=500 \\ x=\frac{500}{48} \end{gathered}$$

So, the amount (in Rs.) paid by B to A

$$\begin{gathered} =120x \\ =(120\times \frac{500}{48}) \\ =1250 \end{gathered}$$

When a person is referred by his designation, instead of his name, then definite article 'The' is used before his designation. Therefore, the correct answer will be- "The Chief Minister will decide the matter soon".

Indefinite article 'an' is used before a singular noun starting with a vowel sound. In the word 'Honest', h is silent. Therefore, its pronunciation starts with sound 'o'. So, 'a' will be replaced by 'an'.

The indefinite article 'an' is used before singular nouns starting with a vowel sound. In this sentence, the word 'universal' is starting with a consonant sound 'yoo' and not with a vowel sound 'uh'. Therefore, 'an' will be replaced by 'a'.

The error lies in first part of the sentence. The definite article 'The' is used before the names of newspapers. For example, The Times, The Hindu, etc. Therefore, in this sentence, The will be used before 'Times of India'.

There is no error in the given sentence. The speaker here is talking about some bus accident of which the listener is not aware. There is no information about the bus service. Therefore, instead of using the definite article 'the', the indefinite article 'a' has been used before the noun bus in the sentence.

The sentence "He behaved though it was his fault, we knew he was not responsible for it" is not correct as of the phrase 'though it' used here is incorrect. The phrase 'though it' does not only make it grammatically incorrect but doesn't add any meaning to the sentence either.
Option (c) here whereas makes the sentence meaningful and grammatically correct as well. Hence, the correct sentence will be, "He behaved as if it was his fault, we knew he was not responsible for it".

The sentence "She never felt that it was not her business to get involved in somebody else's family matter" is not correct due to the phrase ‘was not her business’. The use of 'not her' makes the sentence grammatically incorrect. Instead of 'not her', 'none of her' should be used to make the sentence grammatically meaningful.
Therefore, the second option will be the correct option and the correct sentence will be, "She never felt that it was none of her business to get involved in somebody else's family matter".

The sentence, "Being born in a certain family is not in our control" is grammatically correct. ‘Being’ is a participle that is in perfect coherence with the word ‘born’. It relates to the birth of a person in a family over which one has no choice. Therefore, option (e) is the correct answer. There is no need to make any sort of amendment to the sentence.

The sentence, "I was taken back by his sudden comment on this issue" is grammatically incorrect. The term 'taken back' means literally taken back somewhere (to a different period of time) which is a total misfit in this sentence. Instead of using 'taken back', the term 'taken aback' can be used, which actually means being startled.
Therefore, the correct answer is option d and the correct sentence will be, "I was taken aback by his sudden comment on this issue".

The sentence "In a matter of seconds, we come to know of what is happening anywhere in the world" is not correct as the phrase 'come to know of' used here is incorrect. The phrase 'come to know of' does not only make it grammatically incorrect due to the wrong use of tense but also doesn't add any meaning to the sentence either. Option d here whereas makes the sentence meaningful and grammatically correct.
Hence, the correct sentence will be, "In a matter of seconds, we are coming to know of what is happening anywhere in the world".

'At' is a preposition used to indicate a point or place occupied by someone or something. However, 'with' means accompanied by another person or thing.
Here, the speaker is accompanied by his uncle. Therefore, in the given sentence preposition 'with' should be used.
Hence, the correct option is 3.

'Who' is the doer of the action and generally used as the subject of a sentence. However, 'whom' is used instead of ‘who’ as the object of a verb or preposition. 
So, in the given sentence 'whom' should be used.
Hence, the error is in this part.

The use of has + the third form of the verb i.e., 'reduced'. It tells that the sentence is in the present perfect tense.
The sentence has a main and subordinate clause, connected by 'because' which is a subordinate conjunction.
Therefore, there are no errors in this sentence.

In this sentence, the indefinite pronoun 'everyone' is singular. Therefore, it requires a singular verb 'knows'. 'Know' is used for the plural subject.
Hence, the correct sentence will be: Everyone of us knows that he is not capable of remaining underwater for such a long time.

The given sentence is in the passive voice. A passive sentence always takes the 'be + the third form of the verb'. So, the third form of the verb 'deceive' is 'deceived'.
Therefore, 'that he could not deceive' will be replaced with 'that he could not be deceived'.
Hence, the correct option is 2.

In the given sentence, the speaker is saying that seeing the people in a specified manner will help the person to know who is the culprit so the correct filler is the word 'look'.
'Look' means to see in a specified direction.
Hence, option (a) is the correct answer.

In the given sentence completion question, the speaker is saying that they should buy the ticket in advance. So, the correct filler is 'buy'.
'Buy' means to purchase.
Therefore, the correct option is 2.

In the given sentence completion question, the speaker is saying that family planning is important to prevent the rapid growth in population so the correct filler is the word 'increase'.
'Increase' means to become or make something greater in amount or degree.
Hence, the correct answer is option 2.

In the given sentence completion question, the speaker is saying that his friend put the first pay in the bank so the correct filler is the word 'deposit'.
'Deposit' means to put something in a specific place for safekeeping.
Hence, the correct answer is option 1.

In the given sentence completion question, the speaker is saying that they were having similar characteristics to understand each other without expressing it and it is not verbal so the correct filler is the word 'tacit'.
'Tacit' means understood without being expressed directly.
Hence, the correct answer is option 3.

Fetish is a noun, that means an obsession. Mania means an excessive desire that is similar to fetish in meaning thus it is a synonym. Whereas, gradient means a slope; psychosis means a severe mental disorder and idiocy means madness, these words do not relate to the given word.

Antipathy is a noun, that means an opposition. Aversion means a strong dislike that is similar to antipathy in meaning thus it is a synonym. Whereas sordid means immoral actions; goodwill means friendly and malevolence means hatred, these words do not relate to the given word.

Apocalypse is a noun, that means judgment day or the final destruction of the world or an environmental disaster. Catastrophe means sudden damage or disaster to the environment, which is similar to Apocalypse in meaning thus it is a synonym. Whereas, construction means creation; saviour means a person who saves someone and Demolition means damaging, these words do not relate to the given word.

Charisma is a noun, that means a charm or compelling attractiveness. Magnetism means attraction, which is similar to charisma in meaning thus it’s synonym. Whereas, lucid means easy to understand; cogent means a convincing argument and fascination means interest or passion, these words do not relate to the given word.

Persuasive is an adjective that means influential. Convincing means capable of making someone believe that something is real, that is similar to persuasive in meaning thus it is a synonym. Whereas, push means to apply force; hold on means wait and putting forth
means to make or create, these words do not relate to the given word.

Commission is the correctly spelt word. It is used as a noun or a verb. It refers to ‘an instruction’ or ‘ a group of people given an authority by the government to do something’. And its synonyms are-project, task, committee, board and council.
For example:
A commission is set up in Delhi.

'Committee' is the correctly spelt word. It is used as a noun. It refers to ‘a group of people appointed for a specific function’. And its synonyms are board or panel or bureau.
For example:
The committee is ready with its guidelines.

'Colleague' is the correctly spelt word. It is used as a noun. It refers to ‘a person with whom one works in a profession’. Its synonyms are teammate or co-worker.
For example: Mohan is my colleague, we have been working for this company for more than 5 years.

'Corruptive' is the correctly spelt word. It is used as an adjective that refers to ‘willingness to act dishonestly’. Its synonyms are-dishonest or untrustworthy.
For example: The corruptive officials levied heavy taxes on people.

'Exorbitant' is the correctly spelt word. It is used as an adjective. It refers to 'the unreasonably high price of something’. Its synonyms are excessive and sky-high.
For example: The bill for lunch was exorbitant.

'Would' is a past-tense form of will.
If past events are being discussed then 'would' can be used to indicate something that was in the future at that point in time, but is not necessarily in the future right now. In other words, 'would' is used to preserve the future aspect when talking about the past.
The completed sentence is- When I was training for the marathon, I would run over 100 km a week.

"I know" is the best suitable option. The sentence is in the present tense, hence, the blank should also be in the present tense. With a plural pronoun, a plural verb should be used in option (a). "Who" and "Which" cannot be used before "I know" in option (c) and (d).
The completed sentence is- My colleague is one of the kindest people I know.

Option (C) is the most suitable answer. Advice means guidance or recommendations offered with regard to prudent future action.
In the given question, the lawyer's role was to solve a particular problem. 'Advice' fits the blank perfectly.
The completed sentence- The lawyer's advice led to the resolution of the problem.

Competition in the telecommunication industry will mean a lower price for customers because industries will try to earn more and more customers and for that, they will lower the prices which will benefit the customers.
Option E is the correct choice.
The completed sentence is- The government claims that competition in the telecommunication industry will mean lower prices for customers.