# SBI PO Quantitative Aptitude For Prelims: 16th February

Numerical Ability or Quantitative Aptitude Section has given heebie-jeebies to the aspirants when they appear for a banking examination. As the level of every other section is only getting complex and convoluted, there is no doubt that this section, too, makes your blood run cold. The questions asked in this section are calculative and very time-consuming. But once dealt with proper strategy, speed, and accuracy, this section can get you the maximum marks in the examination. Following is the Quantitative Aptitude quiz to help you practice with the best of latest pattern questions.

**Directions (1-5): In each of the following questions two equations are given. You have to solve the equations and Give answer –**

**Q1. I. 8x² + 18x + 9 = 0**

**II. 4y² + 19y + 21 = 0**

if x < y

if x ≤ y

relationship between x and y cannot be determined

if x ≥ y

if x > y

Solution:

I. 8x² + 18x + 9 = 0

⇒ 8x² + 12x + 6x + 9 = 0

⇒ (2x + 3) (4x + 3) = 0

⇒ x = –3/2, –3/4

II. 4y² + 19y + 21 = 0

⇒ 4y² + 12y + 7y + 21 = 0

⇒ (y + 3) (4y + 7) = 0

⇒ x = –3, –7/4

x >y

⇒ 8x² + 12x + 6x + 9 = 0

⇒ (2x + 3) (4x + 3) = 0

⇒ x = –3/2, –3/4

II. 4y² + 19y + 21 = 0

⇒ 4y² + 12y + 7y + 21 = 0

⇒ (y + 3) (4y + 7) = 0

⇒ x = –3, –7/4

x >y

**Q2. I. 3x² + 16x + 21 = 0**

**II. 6y² + 17y + 12 = 0**

if x < y

if x ≤ y

relationship between x and y cannot be determined

if x ≥ y

if x > y

Solution:

I. 3x² + 16x + 21 = 0

⇒ 3x² + 9x + 7x + 21 = 0

⇒ (x + 3) (3x + 7) = 0

⇒ x = –3, –7/3

II. 6y² + 17y + 12 = 0

⇒ 6y² + 9y + 8y + 12 = 0

⇒ 3y (2y + 3) + 4 (2y + 3) = 0

⇒ y = – 3/2, –4/3

y > x

⇒ 3x² + 9x + 7x + 21 = 0

⇒ (x + 3) (3x + 7) = 0

⇒ x = –3, –7/3

II. 6y² + 17y + 12 = 0

⇒ 6y² + 9y + 8y + 12 = 0

⇒ 3y (2y + 3) + 4 (2y + 3) = 0

⇒ y = – 3/2, –4/3

y > x

**Q3. I. 16x² + 20x + 6 = 0**

**II. 10y² + 38y + 24 = 0**

if x < y

if x ≤ y

relationship between x and y cannot be determined

if x ≥ y

if x > y

Solution:

I. 16x² + 20x + 6 = 0

⇒ 8x² + 10x + 3 = 0

⇒ 8x² + 4x + 6x + 3 = 0

⇒ (2x + 1) (4x + 3) = 0

⇒ x = –1/2, –3/4

II. 10y² + 38y + 24 = 0

⇒ 5y² + 19y + 12 = 0

⇒ 5y² + 15y + 4y + 12 = 0

⇒ (y + 3) (5y + 4) = 0

y = –3, –4/5

x > y

⇒ 8x² + 10x + 3 = 0

⇒ 8x² + 4x + 6x + 3 = 0

⇒ (2x + 1) (4x + 3) = 0

⇒ x = –1/2, –3/4

II. 10y² + 38y + 24 = 0

⇒ 5y² + 19y + 12 = 0

⇒ 5y² + 15y + 4y + 12 = 0

⇒ (y + 3) (5y + 4) = 0

y = –3, –4/5

x > y

**Q4. I. 8x² + 6x = 5**

**II. 12y² – 22y + 8 = 0**

if x < y

if x ≤ y

relationship between x and y cannot be determined

if x ≥ y

if x > y

Solution:

I. 8x² + 6x – 5 = 0

⇒ 8x² + 10x – 4x – 5 = 0

⇒ (4x + 5) (2x – 1) = 0

⇒ x = ½, –5/4

II. 12y² – 22y + 8 = 0

⇒ 6y² – 11y + 4 = 0

⇒ 6y² – 3y – 8y + 4 = 0

⇒ (2y – 1) (3y – 4) = 0

⇒ y = 1/2, 4/3

y ≥ x

⇒ 8x² + 10x – 4x – 5 = 0

⇒ (4x + 5) (2x – 1) = 0

⇒ x = ½, –5/4

II. 12y² – 22y + 8 = 0

⇒ 6y² – 11y + 4 = 0

⇒ 6y² – 3y – 8y + 4 = 0

⇒ (2y – 1) (3y – 4) = 0

⇒ y = 1/2, 4/3

y ≥ x

**Q5. I. 17x² + 48x = 9**

**II. 13y² = 32y – 12**

if x < y

if x ≤ y

relationship between x and y cannot be determined

if x ≥ y

if x > y

Solution:

I. 17x² + 48x – 9 = 0

⇒ 17x² + 51x – 3x – 9 = 0

⇒ (x + 3) (17x – 3) = 0

⇒ x = 3/17, – 3

II. 13y² – 32y + 12 = 0

⇒ 13y² – 26y – 6y + 12 = 0

⇒ (y – 2) (13y – 6) = 0

⇒ y = 2, 6/13

y > x

⇒ 17x² + 51x – 3x – 9 = 0

⇒ (x + 3) (17x – 3) = 0

⇒ x = 3/17, – 3

II. 13y² – 32y + 12 = 0

⇒ 13y² – 26y – 6y + 12 = 0

⇒ (y – 2) (13y – 6) = 0

⇒ y = 2, 6/13

y > x

**Directions (6-8): Each question below is followed by two statements A and B. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer.**

**Q6. Triangle ABC has angle BAC equal to 90°. What is the measure of the angle ABC?**

**A. The angle ACB is 35°.**

**B. The angle CBA is 55°.**

if the statement A alone is sufficient to answer the question, but the statement B alone is not sufficient.

if the statement B alone is sufficient to answer the question, but the statement A alone is not sufficient.

if both statements A and B together are needed to answer the question.

if either the statements A alone or statement B alone is sufficient to answer the question

if you cannot get the answer from the statements A and B together, but need even more data.

Solution:

From statement A

∠ABC = 180 – (∠BAC + ∠ACB)

= 180 – (90+ 35) = 55°

From statement B, ∠ABC = 55°

∠ABC = 180 – (∠BAC + ∠ACB)

= 180 – (90+ 35) = 55°

From statement B, ∠ABC = 55°

**Q7. X, Y and Z are three consecutive even numbers (not necessarily in this order). What is the sum of these numbers?**

**A. The difference between X and Z is 4.**

**B. One-third of Y is 14.**

if the statement A alone is sufficient to answer the question, but the statement B alone is not sufficient.

if the statement B alone is sufficient to answer the question, but the statement A alone is not sufficient.

if both statements A and B together are needed to answer the question.

if either the statements A alone or statement B alone is sufficient to answer the question

if you cannot get the answer from the statements A and B together, but need even more data.

Solution:

A. x - z = 4 or z - x = 4

B. y/3 = 14 ⇒ y = 42

So, nos. are 40, 42, 44

So, both statements together are required to answer the question

B. y/3 = 14 ⇒ y = 42

So, nos. are 40, 42, 44

So, both statements together are required to answer the question

**Q8. What is the salary of P, in a group of P, Q, R, S, T and U, if average salary of group is Rs. 35,000?**

**A. Total of the salary of Q and S together is Rs. 54000.**

**B. Total of the salary of T and U together is Rs. 58000.**

if the statement A alone is sufficient to answer the question, but the statement B alone is not sufficient.

if the statement B alone is sufficient to answer the question, but the statement A alone is not sufficient.

if both statements A and B together are needed to answer the question.

if either the statements A alone or statement B alone is sufficient to answer the question

if you cannot get the answer from the statements A and B together, but need even more data.

Solution:

P + Q + R+ S +T +U = 6 × 35,000 = 210,000

A. Q +S = 54,000

B. T + U = 58,000

P + R = 210,000 – (54,000 + 58,000)

= 210,000 – 112,000

= 98,000

We cannot find salary of P from given data

A. Q +S = 54,000

B. T + U = 58,000

P + R = 210,000 – (54,000 + 58,000)

= 210,000 – 112,000

= 98,000

We cannot find salary of P from given data

**Q9. Quantity 1: Height of the cylindrical tank if the volume of cylindrical tank is 12320 cm³. Its radius and height are in the ratio of 7 : 10 respectively.**

**Quantity 2: Level of kerosene in the cylinderical jar. The conical vessel of base radius 2 cm and height 3 cm is filled with kerosene. This liquid leak through a hole in the bottom and are being collected in a cylindrical jar of radius 2 cm.**

Quantity I > Quantity II

Quantity I < Quantity II

Quantity I ≥ Quantity II

Quantity I ≤ Quantity II

Quantity I = Quantity II or No relation

**Q10. A man who swims 48m/minute in still water, swims 200m against the current and 200m with the current. The difference of time in travelling these 200m in upstream and downstream is 10 minutes.**

**Quantity 1: speed of current.**

**Quantity 2: Speed of a man who completes 3 rounds of a circular path of radius 49 m in 14 minutes.**

Quantity I > Quantity II

Quantity I < Quantity II

Quantity I ≥ Quantity II

Quantity I ≤ Quantity II

Quantity I = Quantity II or No relation

**Directions (11-15): Given below is the data related to Candidates appeared and qualified in UPTET 2018 exam from 6 different cities of UP.**

Table also shows the ratio of boys to girls appeared and qualified.

**Q11.Girls appeared from city Ghazipur is what percent of girls qualified from city Unnao?(Round off to 2 decimal places)**

54.54%

52.56%

51.58%

56.58%

48.58%

**Q12. Find the ratio of boys appeared from city Ghazipur and city Ghaziabad together to the girls qualified from the same cities.**

5 : 4

4 : 3

3 : 2

2 : 1

1 : 2

**Q13. Boys appeared from city Ghaziabad is what percent of average no. of Students appeared from all cities?**

50%

30%

35%

40%

45%

**Q14. If 100/9% of girls qualified from city Jaunpur were found not eligible to get appointed as a primary teacher in the schools due to some reasons, then find the ratio between girls appointed as primary teacher in various schools through UPTET from Jaunpur to the total number of students qualified from Jaunpur.**

8 : 23

7 : 23

15 : 8

8 : 15

23 : 8

**Q15. Find the total number of girls qualified from all cities together.**

2652

2742

2826

2761

2736

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