Mental Ability Questions & Answers (Compiled from UPSC, SSC ,PSC ,IBPS previous question papers)

I. x²-4x-12 = 0

⇒  x²-6x+2x-12=0

⇒ x(x-6)+2(x-6) = 0

⇒ (x-6)(x+2)=0

⇒ x = -2,6

II. y²-5y-14=0

⇒ y²-7y+2y-14 = 0

⇒ y(y-7)+2(y-7)=0

⇒ (y-7)(y+2)=0

⇒ y = -2,7

∴ x≤y

Let the initial investment of A = 18x

And initial investment of B = 7x

According to question,

18x×4+(18x+2000)×8/7x×4+(7x+7000)×8 = 2/1

⇒ 18x+(18x+2000)×2 = 2×[7x+(7x+7000)×2]

⇒ 9x+18x+2000 = 7x+14x+14000

6x = 12000

x=2000

∴ Total initial investments of A and B

 = 18x+7x = 25x = 25×2000

 = INR 50000

Required percentage = 21-15/15×100 = 40%

Number of laptops (both Dell and Lenovo) sold by store Q = 4500×23/100 = 45×23 = 1035

Number of laptops (both Dell and Lenovo) sold by store R and store S together = 4500×46/100 = 2070

Number of Dell laptops sold by store R and store S together = 2400×39/100 = 936

Number of Lenovo laptops sold by store R and store S together = 2070-936 = 1134

∴ Required difference = 1134-1035 = 99

Number of Dell laptops sold by store Q

=2400×25/100 = 600

Number of laptops (both Dell and Lenovo) sold by store R = 4500×35/100=1575

∴ Required percentage = 600/1575 × 100 = 38%

Required central angle = 9/100×360 = 32.4⁰

The average number of Dell laptops sold by P, R and S together = 2400×(15+30+9)/100×1/3

=8×54 = 432

3(×1+2) 5 (×2+3) 13(×3+4)  43(×4+5)  177(×5+6)891

1(×1+1)³ 2 (×2+2)³12(×3+3)³ 63(×4+4)³ 316(×5+5)³ 1705

100(÷2+2)52(÷2+2) 28(÷2+2) 16(÷2+2) 10 (÷2+2)7

9(×0.5-0.5)4(×1+1)5(×1.5-1.5)6(×2+2)14(×2.5-2.5)32.5

500-16 = 484

484-33(=16+1×17) = 451

451-67(=33+2×17)=384

384-118(=67+3×17)=266

266-186(=118+4×17)=80

Remaining mixture in vessel = 100-40 = 60 litre

Quantity of milk = 60×22/25 = 52.8 litre

Quantity of water = 60-52.8 = 7.2 litre

4.8 litre of each pure milk and pure water is added to the mixture.

Then,

Quantity of milk = 52.8+4.8 = 57.6 litre

Quantity of water = 7.2+4.8 = 12 litre

∴ Required percentage = 57.6-12/57.6×100

=45.6/57.6×100 = 79 1/6%

500-16=484

Let the rate of interest be r.

According to question,

P×r×r/100 = P[(1+r/100)²-1]

⇒ r²/100 =1+r²/10000+2r/100-1

⇒ r²/100 =r²/10000+r/50

⇒r/100=r/10000+r/50

⇒r/100-r/10000=1/50

⇒99r/10000=1/50

99r = 200

r = 200/99 = 2 2/99%

Let the number of failed students = x

The number of passed students = 50-x

According to question,

50×34=x×16+52(50-x)

⇒1700=16x+2600-52x

⇒36x=900

⇒x=25

Let present age of Y =a

Present age of X = 3a+3

Present age of Z = 2a

According to question,

3a+3-2a = 12

a=12-3=9

∴Z's present age = 2 × 9 =18 years

Let marked price = INR x

S.P. of item = x × 80/100×110/100 = 22x/25

For retailer,

S.P. = 22x/25×125/100 = 11x/10

According to question,

11x/10-22x/25 = 2046

55x-44x/50 = 2046

11x = 2046×50

x = 186×50

x = INR 9300/-

Total number of balls = 3+5+7 = 15

∴ Probability of either pink or red ball

 = ⁷C₁+³C₁/¹⁵C₁

=7+3/15= 10/15 = 2/3

Let the height and the radius of cylinder be h cm and rcm respectively.

According to question, 

2Πrh/2Πrh[r+h] = 4/5

⇒ 5h = 4r+4h

⇒ h = 4r

Curved surface area of cylinder = 1232

2Πrh = 1232

2×22/7×h/4×h = 1232

h² = 28×28

h = 28 cm

8(×1/2)4(×3/2)6(×5/2)15(×2/2)52.5(×9/2)236.25

3(×1+1)4(×2+1)9(×3+1)28(×4+1)113(×5+1)566

320-((1³-1)=0)320((-2³-2)=-6)314((-3³-3)=-24)290-((4³-4)=-60)230-((5³-5)=-120)110

190-96=94-48=46-24=22-12=10-6=4

123+17=140-34=106+51=157-68=89+85=174

Let total amount = INR x

Amount received by A  = x/2+40

Amount received by B = 3x/8-120

According to question,

⇒x-[x/2+40]-[3x/8-120]=200

⇒8x-4x-3x/8 - 40+120=200

⇒x/8=200-80

⇒x=120×8

⇒x=INR 960/-

Ratio of milk and water = 80:18 = 40:9

Total quantity of mixture = 80+18 = 98 litre

According to question,

49×40/49 + 2x/49×9/49+x = 4/1

40+2x = 36+4x

2x=4

x = 2 litre

∴ Quantity of pure milk added in the vessel

= 2x = 2×2 = 4 litre

28 men can do a work in 15 days.

Work done by 28 men in 1 day = 1/15

Work done by 1 man in 1 day = 1/15×28

Work done by 30 men in 1 day = 30 /15×28 = 1/24

15 women can do a work in 24 days 

Work done by 15 women in 1 day  = 1/24

Work done by 1 woman in 1 day = 1/15×24

Work done by 18 women in 1 day 

=18/24×15 = 1/20

∴ Required ratio = 1/14:1/20 

=10:7

Let the distance between A and B = x km,

According to question,

x/5-x/8 = (48+15)/60

⇒ 8x-5x / 40 = 63/60

⇒3x/40 = 63/60

⇒x = 63×40/60×3 

⇒x = 14km

A:B:C = 4x×12:6x×8:5x×8 = 6:6:5

According to question,

6x-5x = 250

x= 250

∴ Total annual profits = 250×(6+6+5) = INR 4250/-

I. x² = 16 ⇒ x = ± 4 ⇒ x = 4, -4

II. 2y²-17y+36=0

⇒ 2y(y-4)-9(y-4) = 0

(2y-9)(y-4)( = 0

⇒ y = 9/2,4

∴ x ≤ y