Quant Question of the Day Chat : Quantitative Questions

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Arpit_Bhardwaj

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31 Jul 2023, 11:03

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gmatophobia

DS Question 1 - July 31 The integers n and t are positive and n > t > 1. How many different subgroups of t items can be formed from a group of n different items? (1) The number of different subgroups of n − t different items that can be formed from a group of n different items is 680. (2) nt = 51 Source: Kaplan | Difficulty: Hard

we need to find n/t as per the question.

Statement 1

n/(n-t) = 680

we can find n/t here hence it is sufficient to answer the question.

Statement 2

n*t= 51 = 3*17

we can say n=17 and t=3 from here. because n>t>1 and hence we can deduce it directly.

we can find n/t here hence it is sufficient to answer the question.

Hence (D) Each alone is sufficient.

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31 Jul 2023, 11:10

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Arpit_Bhardwaj

we need to find n/t as per the question. Statement 1 n/(n-t) = 680 we can find n/t here hence it is sufficient to answer the question. Statement 2 n*t= 51 = 3*17 we can say n=17 and t=3 from here. because n>t>1 and hence we can deduce it directly. we can find n/t here hence it is sufficient to answer the question. Hence (D) Each alone is sufficient.

We are asked the number of subgroups that can be formed. n/t would give us the ways of distributing n things to t places/people?

For example n=3 t= 2
So 3 numbers lets say 1 2 3 into 2 sub groups would be 1 2, 23, 13 which is 3 not 3/2. Thoughts?

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31 Jul 2023, 11:10

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Arpit_Bhardwaj

Approach is if we think of 3:20am as a loop of time of 24 hours. The clock starts going in reverse direction in double speed so when we move x hours forward in time the clock goes 2x hours in reverse. And the point where these two meets for the first time shall be our answer. And after 8 hrs the actual time will move forward 8 hrs while the clock will move 16 hrs in reverse direction to meet the actual time. So 3:20am+8hrs = 11:20am.

Did you calculate 8 hrs and 16hrs manually? As in, did you check for every hour forward, if 2 hours in reverse match with it? Or did you arrive at 8 and 16 with by applying any other logic?

Never mind, I just got what you’re saying. 8+16 = 24 hours, yes?

which is x and 2x

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31 Jul 2023, 11:13

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Dumsy_1711

Did you calculate 8 hrs and 16hrs manually? As in, did you check for every hour forward, if 2 hours in reverse match with it? Or did you arrive at 8 and 16 with by applying any other logic?

Arrived it through logic as I said its a loop of 24 hours and if actual time goes x in forward the the clock would go 2x in reverse direction and sum both x+2x = 24 as only on that point they would meet. So x = 8 hours.

We can do it manually too but I guess that will be more hectic and time consuming as we have to do it with 2-3 mins.

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31 Jul 2023, 11:15

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Thanks, Arpit.

It looks so simple once you came up with an explanation, and yet, I couldn’t think of any way of addressing it other than checking it hour by hour

Definitely bookmarking your post for later

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31 Jul 2023, 11:18

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Dumsy_1711

Thanks, Arpit.

It looks so simple once you came up with an explanation, and yet, I couldn’t think of any way of addressing it other than checking it hour by hour

You are welcome Dumsy_1711.

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31 Jul 2023, 11:26

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D is a 3 digit number such that ratio of number to the sum of it’s digits is least. What is the difference between the digit at hundred’s place and the digit at unit’s place?

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31 Jul 2023, 11:31

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Divyaas

We are asked the number of subgroups that can be formed. n/t would give us the ways of distributing n things to t places/people? For example n=3 t= 2 So 3 numbers lets say 1 2 3 into 2 sub groups would be 1 2, 23, 13 which is 3 not 3/2. Thoughts?

Hey I guess you are right and even if we go by permutation and combination the answer comes out to be same as (D). Its a little unclear to me as to if it means we need to tell in how many ways we can form subgroups or we need to tell how many subgroups we can form.

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31 Jul 2023, 11:35

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Arpit_Bhardwaj

Hey I guess you are right and even if we go by permutation and combination the answer comes out to be same as (D). Its a little unclear to me as to if it means we need to tell in how many ways we can form subgroups or we need to tell how many subgroups we can form.

How many different subgroups can be formed?

And yes, you are right the answer is D anyways.

Arpit_Bhardwaj

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31 Jul 2023, 11:40

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How many different subgroups can be formed?

One interpretation is of choosing and making subgroups like you illustrated above.

Second interpretation that I did while reading the question was how many different subgroups with t items can be formed with n different items.n=10 and t=2 So like how many different subgroups can be formed of 2 items from 10 different items.

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31 Jul 2023, 11:47

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Arpit_Bhardwaj

How many different subgroups can be formed? One interpretation is of choosing and making subgroups like you illustrated above. Second interpretation that I did while reading the question was how many different subgroups with t items can be formed with n different items.n=10 and t=2 So like how many different subgroups can be formed of 2 items from 10 different items.

Right
Generally sets brings in the idea of subgroups to me. But this question doesn’t have that. So even I am not sure how to point that out.

Arpit_Bhardwaj

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31 Jul 2023, 11:51

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Divyaas

Right Generally sets brings in the idea of subgroups to me. But this question doesn’t have that. So even I am not sure how to point that out.

Yeah and generally a P&C question contains "in how many ways" or specially a sense of choosing or forming groups. Also generally dividing a group into subgroups would simply mean to divide then and not like choose and form different ways of forming just one subgroup.

Arpit_Bhardwaj

Yeah and generally a P&C question contains "in how many ways" or specially a sense of choosing or forming groups. Also generally dividing a group into subgroups would simply mean to divide then and not like choose and form different ways of forming just one subgroup.

I can be wrong though but this is my observation uptill now.

Divyaas

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31 Jul 2023, 11:56

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Thanks for your inputs. 😋

Arpit_Bhardwaj

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31 Jul 2023, 11:59

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Divyaas

Thanks for your inputs. 😋

Sure and thanks for pointing it out.

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31 Jul 2023, 12:51

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gmatophobia

DS Question 1 - July 31 The integers n and t are positive and n > t > 1. How many different subgroups of t items can be formed from a group of n different items? (1) The number of different subgroups of n − t different items that can be formed from a group of n different items is 680. (2) nt = 51 Source: Kaplan | Difficulty: Hard

d - 1. n C T = n C n-t suff 2. only possible n =17 t =3 suff

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01 Aug 2023, 05:35

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Jim needs to mix a solution in the following ratio: 1 part bleach for every 4 parts water. When mixing the solution, Jim makes a mistake and mixes in half as much bleach as he ought to have. The total solution consists of 18 mL. How much did Jim put into the solution?

A. 1mL
B. 2mL
C. 3mL
D. 4mL
E. 5mL

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01 Aug 2023, 06:09

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Mapat

D is a 3 digit number such that ratio of number to the sum of it’s digits is least. What is the difference between the digit at hundred’s place and the digit at unit’s place?

Correct me if I’m wrong, but if the ratio is least, Then we need to make sure D/(sum of digits) of D is least.
100 is the smallest 3 digit number, but the sum of its digit is small too. To get the smallest ratio, let’s consider this:
999 is the largest number, but the sum of its digits is very large.
On the other hand 199 is a small 3 digit number whose sum of digits is large enough to minimise the ratio (1+9+9 = 19).
Therefore, D = 199.
(D/19 ~= 10.4)
Difference between the hundreds and units place = 8.

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