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sarphant123
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From the set {10,12,14,17}, how many two-n 27 Jul 2020, 00:03
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35% (medium)

Question Stats:

61% (01:04) correct 39% (01:00) wrong based on 345 sessions

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From the set {10,12,14,17}, how many two-number subsets can be formed that do not contain the pair of numbers 10 and 17?
(A)1
(B)2
(C)4
(D)5
(E)6
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D
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EgmatQuantExpert
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From the set {10,12,14,17}, how many two-n 27 Jul 2020, 01:08
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Solution


Given

    • A set contains the numbers {10,12,14,17}.

To Find

    • The number of 'two-number subsets' that do not contain the pair of numbers 10 and 17.

Approach and Working Out


    • Total number of subsets = 4C2
      = 6
    • The subset we cannot take is 1 {10,17}
    • The number of subsets we can take is 6 – 1
      = 5


Correct Answer: Option C
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From the set {10,12,14,17}, how many two-n 27 Jul 2020, 01:28
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Quote:
From the set {10,12,14,17}, how many two-number subsets can be formed that do not contain the pair of numbers 10 and 17?
Show more
Step 1: Understanding the question
The set has four values, from which two values are to be picked.
As the order of selecting two value out of four values do not matter, hence the question is on Combination

Step 2: Calculation
Total number of subsets = Number of ways to select two values out of four values = 4C2 = \(\frac{4!}{2!*2!}\) = 6

Number of pair which has {10, 17} is 1

Hence, Number of subsets which do not have a set of {10,17) = 6 -1 = 5

C is correct

Link to my video on the topic: Combination
https://youtu.be/OnqHOLkCqSE
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From the set {10,12,14,17}, how many two-n 25 Aug 2021, 19:22
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EgmatQuantExpert

Solution


Given

    • A set contains the numbers {10,12,14,17}.

To Find

    • The number of 'two-number subsets' that do not contain the pair of numbers 10 and 17.

Approach and Working Out


    • Total number of subsets = 4C2
      = 6
    • The subset we cannot take is 1 {10,17}
    • The number of subsets we can take is 6 – 1
      = 5


Correct Answer: Option C
Show more


Hi - why cant we use the cases approach wherein,

Case 1:does not have 10 -> 3C2 = 3

Case 2: does not have 17 -> 3C2=3

total = 6?
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From the set {10,12,14,17}, how many two-n 26 Aug 2021, 05:18
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EgmatQuantExpert

Solution


Given

    • A set contains the numbers {10,12,14,17}.

To Find

    • The number of 'two-number subsets' that do not contain the pair of numbers 10 and 17.

Approach and Working Out


    • Total number of subsets = 4C2
      = 6
    • The subset we cannot take is 1 {10,17}
    • The number of subsets we can take is 6 – 1
      = 5


Correct Answer: Option C
Show more
]

Why cant we calculate the total subsets for this as 4 x 3?
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kelbyandrews
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From the set {10,12,14,17}, how many two-n 31 Aug 2021, 07:23
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EgmatQuantExpert

Solution


Given

    • A set contains the numbers {10,12,14,17}.

To Find

    • The number of 'two-number subsets' that do not contain the pair of numbers 10 and 17.

Approach and Working Out


    • Total number of subsets = 4C2
      = 6
    • The subset we cannot take is 1 {10,17}
    • The number of subsets we can take is 6 – 1
      = 5


Correct Answer: Option C
Show more

Can someone tell me where it implies that repetition is not allowed? Here is what I did.
4*4 (2 spots, 4 numbers for each spot) / 2! = 8 total number of opportunities
Then you subtract out the subsets with 10 and 17 {10,17}

Hence 8-1 = 7.
Is this correct or did I miss something?
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lakshya14
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kelbyandrews
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Solution


Given

    • A set contains the numbers {10,12,14,17}.

To Find

    • The number of 'two-number subsets' that do not contain the pair of numbers 10 and 17.

Approach and Working Out


    • Total number of subsets = 4C2
      = 6
    • The subset we cannot take is 1 {10,17}
    • The number of subsets we can take is 6 – 1
      = 5


Correct Answer: Option C

Can someone tell me where it implies that repetition is not allowed? Here is what I did.
4*4 (2 spots, 4 numbers for each spot) / 2! = 8 total number of opportunities
Then you subtract out the subsets with 10 and 17 {10,17}

Hence 8-1 = 7.
Is this correct or did I miss something?
Show more

This is a set question. And the subsets are asked to derive. Although you would be given that repetition is not allowed, in subsets, it will not be stated because subsets means that how many unique sets can be derived from the given set.

Therefore we do not have the liberty in subsets, otherwise in other combination questions, repetition can be used unless stated.
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PolarisTestPrep
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From the set {10,12,14,17}, how many two-n 31 Aug 2021, 22:52
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Hey,

There are so few numbers in question here, you can actually write out all of the possibilities

What are all of the possible pairs besides 10 and 17?

10, 12
10, 14
17, 12
17, 14
12, 14

5 possible subsets

The answer is D
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From the set {10,12,14,17}, how many two-n 16 Dec 2025, 23:44
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What is the question really asking?

“How many two-number subsets can be formed ...”

The keyword is subset.

What a subset means (very important)

A subset is a set, and sets do not have order.

So:

{10, 12} is the same subset as {12, 10}

They are not counted separately

Order matters only if the problem asks for sequences or ordered pairs.
Order does NOT matter if the problem asks for subsets, groups, or selections.
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