Let us calculate total 2’s in the units place. (122, 132, 142 … 192), (201, 212, 222, … 292), (302, 312, … 372) = 8 + 10 + 8 = 26

Total 2’s in tenth’s place, (120, 121, 122, …, 129) + (220, 221, …, 229) + (320, 321, …, 329) = 30

Total 2’s in hundred’s place = (200, 201, … 299) = 100.

Total 2’s between 112 and 375 = 26 + 30 + 100 = 156

Alternate

AS we have to find between 112 and 375 ,so we will not include 112 and 375.

2 at Unit's digit =( 372 - 112 )/10 = 260/10 = 26

Then, As for tens digit ,numbers are : 120,121,122,…129 ,220,221,222,…229 and 320,321,322..329

So ,2 at ten’s digit = 30

And for hundreds digit

Numbers will be 200 ,201,202,203…….299(total 100)

Means

2 at hundred’s digit = 100

Total numbers of 2s between 112 and 375 will be 26 + 30 + 100 = 156

Let Sandra, David and Mary each has s, d and 11 respectively.
After the first distribution,
David has d + d = 2d, Mary has 11 + 11 = 22 and Sandra has s – d – 11.
After the second distribution,
Sandra has 2×(s – d – 11) , mary has 2×22 = 44 and david has 2d – (s – d – 11) – 22=3d – s –11.
After the third distribution,
Sandra has 2×2(s – d – 11), david has 2×(3d – s – 11) and mary has 44 – 2(s – d – 11) – (3d – s – 11) = 77 – s – d
It is given that finally Mary has Rs.17. So, 77 – s – d=17
⇒ s + d = 60
⇒ s + d + 11 = 60 + 11 = 71.

Given that
30L + 3Q = 1167
30L + 6Q = 1284
Solving we get Q = 39, L = 35
So cost of first 10 kgs of apples = 35 × 10 = 350

Numbers which dont have 2 from 1 to 9 = 8
Numbers which don’t have 2 from 10 to 99:
Let us take two places _ _. Now left most place is fixed in 8 ways. Units place is filled with 9 ways. Total 72 numbers.
Numbers which don’t have 2 from 100 to 999 =_ _ _ = 8 × 9 × 9 = 648
Numbers which don’t have 2 from 1000 to 1099 =10_ _ = 9 × 9 = 81
Finally 1100 does not have 2. So 1.
Total number with no 2 in them = 8 + 72 + 648 + 81 + 1= 810
Tickets with 2 in them = 1100 – 810 = 290
Required probability = 290 / 1100

Sol:- As all are contradictory statements, it is clear that ONLY one of them is telling the truth. So remaining 4 of them are lying. Querishi mentioned that exactly 4 are lying. So, he is telling the truth.

Explanation: Let us 1st assume that Uma is telling the truth. Then according to her only one is lying. But if only one is lying then all the others’ statements are contradicting the possibility. If we assume the Querishi is telling the truth, according to him exactly 4 members are lying. So all the others are telling lies and he is the one who is telling the truth. This case fits perfectly.

Let the total work = 120 units.
As George completes this entire work in 8 hours, his capacity is 15 units /hour
Similarly, the capacity of paul is 12 units / hour
the capacity of Hari is 10 units / hour
All 3 started at 9 am and worked upto 11 am. So total work done upto 11 am = 2 x (15 + 12 + 10) = 74
Remaining work = 120 – 74 = 46
Now this work is to be done by paul and hari. 46 / (12 + 10) = 2 hours (approx)
So work gets completed at 1 pm

Arranging the words of waiting in Alphabetical Order : A,G,I,I,N,T,W
Start with A_ _ _ _ _ _ This can be arranged in 6!/2! ways=720/2=360 ways
so can’t be arranged starting with A alone as it is asking for 32nd word so it is out of range
AG_ _ _ _ _then the remaining letters can be arranged in 5!/2! ways so,120/2=60 ways. Out of range as it has to be within 32 words.
AGI_ _ _ _ Now the remaining letters can be arranged in 4! ways =24
AGN _ _ _ _ can be arranged in 4!/2! ways or 12 ways
so,24+12 =36th word so out of range. So we should not consider all the words start with AGN
now AGNI_ _ _can be arranged in 3! ways =6 ways
so 24+6=30 within range
Now only two word left so, arrange in alphabetical order.
AGNTIIW – 31st word
AGNTIWI – 32nd word

It is 114 not 144.
3m + 4a = 85 ..(1)
5a + 6p = 122 ..(2)
6m + 2p = 114 ..(3)
(1) x 2 => 6m + 8a = 170
(3) => 6m + 2p = 114
Solving we get 8a – 2p = 56 ..(4)
(2) => 5a + 6p = 122

3 x (4) = 24a – 6p = 168
Solving we get a = 10, p = 12, m = 15
So a + p + m = 37

Let say maximun marks =100m

Luva got 45m

Kusha got 60m

Let say cut off mark =x

Then 45m =x-4

&60m = x+8

15m =12

5m = 4

100m = 80

Max marks =80

850/50 = 17

So there are 17, Rs. 50 notes.

400/20 = 20

So there are 20, Rs. 20 notes

Probability of selection of purse out of 2 is 0.5.

Probability wil be maximized when in 1 of the purse you keep only 1 Rs. 50 notes. So if that purse is selected, you will definitely find Rs. 50 note. And put all remaining notes in other purse.

Purse 1 :- 1 Rs. 50 Note

Purse 2:- 16 Rs. 50 Note, 20 Rs. 20 Note

So, Probability = 0.5 x 1 + 0.5 x (16/36) = 0.5 + 0.222 = 0.722

Purse 1 will have 50 x 1 - Rs. 50

Purse 2 will have 50 x 16 + 20 x 20 - 800 + 400 - Rs. 1200

Initially:
Alcohol=15l
water=0l

after 1st removal:
alcohol removed=5l
alcohol remaining=10l
water added=5l
alcohol:water=10:5=2:1

after 2nd removal:
solution removed= 5l
amount of alcohol in soln removed=5*2/3=10/3
amount of water in soln removed=5*1/3=5/3
alcohol remaining=10-10/3=20/3
water remaining=5-5/3+5=25/3
alcohol:water=20:25=4:5

Distance covered by police is 5*50=200km.
The Fugitive covered the same distance in 4+5=9hours.
so, the avg. speed of BMW is 250/8=27.79kmpph.

Currently there is no PrepInsta Explanation.

'Ignorance is a bliss and the ignorance of Miranda was really astounding.'
No article is required in the first blank because ignorance is an abstract noun while in the second blank, 'the' shall be used because the second part is about a specific person's ignorance.
No article, the is the correct option.

Answer - simile
We know it's a simile when there is the word 'like' in a sentence. Comparing two things with the use of 'like'

August:- respected and impressive.

Being dignified entails acting in a calm, serious manner that inspires others to respect you.

Here, Dignified is the synonym of AUGUST

Baffling: extremely confusing or difficult to understand.

Cleared up (of the weather) means to become brighter.

S1 is followed by Q as it says about the first man. Q is followed by R as it talks about the second man. R is followed by P as it talks about their going to a coffee shop together. P is followed by R, and finally S as they state their next steps. Hence, the correct order is QRPS

As the given sentence is correct so no error.

It will be crouched down instead of crouched towards.

Challenges must be overcome to realize the potential of a greater regional economic integration.  It will not be suppressed.

Make out should be there as follows to look carefully, can't you make out the resemblance between the mother and the daughter.