Last visit was: 27 Apr 2026, 23:17

It is currently 27 Apr 2026, 23:17

Toolkit

Practice Tests

Data Insights Questions

Data Sufficiency (DS)

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more

Request Expert Reply

Confirm Cancel

Apr 28
Join - GMAT Day!
08:00 AM PDT
-
11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
Apr 27
Try OnDemand GMAT Masterclass
11:00 AM EDT
-
12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors

Back to Forum

Create Topic

GMAT Club Olympics 2025 (Day 1): Ann and Bob each randomly select an

1 2 3 4 5 6 7

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 27 Apr 2026

Posts: 109,948

Own Kudos:

811,641

[28]

Given Kudos: 105,925

Products:

Expert

Expert reply

Posts: 109,948

Kudos: 811,641

[28]

30 Jun 2025, 08:00

Kudos

Bookmarks

00:00

Start Timer

Pause Timer

Resume Timer

Show Answer

Hide

Show

History

Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

57% (01:31) correct

43% (01:36) wrong

based on 791 sessions

History

Date

Time

Result

Not Attempted Yet

Ann and Bob each randomly select an integer from the integers x to y, inclusive. What is the probability that the integer Ann selects is greater than the one Bob selects?

(1) y - x = 9
(2) y = -20

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

Show Answer

Official Answer

Most Helpful Reply

Bunuel

Math Expert

Joined: 02 Sep 2009

Last visit: 27 Apr 2026

Posts: 109,948

Own Kudos:

811,641

[9]

Given Kudos: 105,925

Products:

Expert

Expert reply

Posts: 109,948

Kudos: 811,641

[9]

30 Jun 2025, 08:30

Kudos

Bookmarks

GMAT Club Official Explanation:

Ann and Bob each randomly select an integer from the integers x to y, inclusive. What is the probability that the integer Ann selects is greater than the one Bob selects?

(1) y - x = 9

This implies they are choosing a number from a set of 10 integers, for example, from 1 to 10, inclusive.

Then:

Total outcomes = 10 * 10 = 100
Equal cases (both choose the same number) = 10
Remaining cases = 90
Out of those 90, half will have Ann’s number < Bob’s, and half will have Ann’s number > Bob’s.
So, required probability = 45/100 = 9/20

As you can see, the only thing we needed to know is the sample size. Sufficient.

(2) y = -20

This is clearly insufficient. We have no idea how many integers they’re choosing from.

Answer: A.

General Discussion

MaxFabianKirchner

Joined: 02 Jun 2025

Last visit: 12 Jul 2025

Posts: 65

Own Kudos:

[2]

Given Kudos: 122

Status:26' Applicant

Location: Denmark

Concentration: Finance, International Business

Schools: ESSEC MiF '26 ESADE HEC Imperial LBS Oxford MFE '26 Sloan (MIT) NYU Stern NUS Bocconi IE'26

GPA: 4.0

WE:Other (Student)

Schools: ESSEC MiF '26 ESADE HEC Imperial LBS Oxford MFE '26 Sloan (MIT) NYU Stern NUS Bocconi IE'26

Posts: 65

Kudos: 63

[2]

30 Jun 2025, 08:17

Kudos

Bookmarks

Let `N` be the number of integers from x to y. `N = y - x + 1`.

There are 3 possibilities: Ann's number is greater, Bob's is greater, or they are the same (a tie).

By symmetry, P(Ann > Bob) = P(Bob > Ann).

The probability of a tie is 1/N.

The formula for the probability that Ann's number is greater is (N-1) / (2N). So, if we can find N, we can solve the problem.

(1) y - x = 9

This allows us to find the number of integers: N = (y - x) + 1 = 9 + 1 = 10.
Since we have a specific value for N, we can find the exact probability.

This statement is SUFFICIENT.

(2) y = -20

This gives us the end of the range, but not the start (x). We don't know if the range is 2 integers or 200.

We cannot find N.

This statement is INSUFFICIENT.

Thus, statement (1) alone is sufficient.

The correct answer is (A).

Cana1766

Joined: 26 May 2024

Last visit: 27 Apr 2026

Posts: 85

Own Kudos:

[3]

Given Kudos: 12

Posts: 85

Kudos: 80

[3]

30 Jun 2025, 08:18

Kudos

Bookmarks

I got this question wrong, but actually, the first option is sufficient.
We can actually find favourable outcomes for Ann from the first option, since from the first option,we now know there are ten consecutive numbers.
And if we do 10C2 we get combinations of two numbers chosen from the list.
For example, in 1,2,3,4,5,6,7,8,9,10.The combination of {3,7} where ann chooses 3,she loses,but if you reverse its
{7,3} Ann wins.
So for each combination of numbers, Ann wins.
So the total favourable outcomes is 10C2.

However in the second option there is no range,and hence not sufficent.

anuraagnandi9

Joined: 25 Mar 2025

Last visit: 21 Jan 2026

Posts: 11

Own Kudos:

[2]

Given Kudos: 3

Location: India

GMAT Focus 1: 705 Q87 V84 DI84 Verified score

GPA: 3.34

GMAT Focus 1: 705 Q87 V84 DI84 Verified score

Posts: 11

Kudos: 12

[2]

30 Jun 2025, 08:20

Kudos

Bookmarks

1) y - x = 9
This tells us the range has 10 integers, but we don’t know the actual values of x and y.
The probability depends only on the number of possible values, not which ones.
We can compute the exact probability from this info.
A is sufficient, (it could be A or D at this point)

2) this just gives upper limit, so we have nothing on probability
This is insufficient, hence A would be the answer.

Duongduong273

Joined: 08 Apr 2023

Last visit: 03 Feb 2026

Posts: 32

Own Kudos:

[2]

Given Kudos: 4

Posts: 32

Kudos: 32

[2]

30 Jun 2025, 08:20

Kudos

Bookmarks

A. Because (2) gives y alone is not sufficient. (1) y-x=9 -> Probability = y-x/2(y-x+1) = 9/20

Ann and Bob each randomly select an integer from the integers x to y, inclusive. What is the probability that the integer Ann selects is greater than the one Bob selects?

Quote:

(1) y - x = 9
(2) y = -20

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

Rohit_842

Joined: 01 Feb 2024

Last visit: 27 Apr 2026

Posts: 118

Own Kudos:

Given Kudos: 117

Posts: 118

Kudos: 33

30 Jun 2025, 08:20

Kudos

Bookmarks

The probability depends on whether x & y are equal or not. If they are equal probability becomes 0, if not 1 would be greater than anyways.
St 1 tells us that both are unequal and hence sufficient.
S2 only tells about y, so x may or may not be equal to, hence insufficient

Redmaster2

Joined: 11 Mar 2025

Last visit: 02 Mar 2026

Posts: 52

Own Kudos:

Given Kudos: 105

Posts: 52

Kudos: 25

30 Jun 2025, 08:27

Kudos

Bookmarks

otal number of ordered pairs (Ann’s pick, Bob’s pick) = n · n = n2.
Number of those pairs with Ann’s pick > Bob’s pick = the number of 2-element subsets of the n values, since each unordered pair {a, b} with a ≠ b yields exactly one ordered pair (a, b) with a > b. That count is C(n, 2) = n(n – 1)/2.
Therefore
P(Ann > Bob) = [n(n – 1)/2] / n2 = (n – 1)/(2n).

Statement (1): y – x = 9 ⟹ n = 10 ⟹ P = (10 – 1)/(2·10) = 9/20. ⇒ sufficient.
Statement (2): y = –20 fixes only y, leaves x (and hence n) unknown. ⇒ not sufficient.

Kinshook

Major Poster

Joined: 03 Jun 2019

Last visit: 27 Apr 2026

Posts: 5,988

Own Kudos:

5,861

[2]

Given Kudos: 163

Location: India

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

WE:Engineering (Transportation)

Products:

Schools: HBS '26 CBS '26 Wharton '26

GMAT 1: 690 Q50 V34 Verified score

Posts: 5,988

Kudos: 5,861

[2]

30 Jun 2025, 08:27

Kudos

Bookmarks

Ann and Bob each randomly select an integer from the integers x to y, inclusive.

What is the probability that the integer Ann selects is greater than the one Bob selects?

(1) y - x = 9; y = x+9
Integers = {x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, x+9}
Total cases = 10*10 = 100
Let the number of cases when Ann selects is greater than the one Bob selects = The number of cases when Bob selects is greater than the one Ann selects = x
The number of cases when both select the same integers = 10
2x + 10 = 100
x = 45
The probability that the integer Ann selects is greater than the one Bob selects = 45/100
SUFFICIENT

(2) y = -20
Since x is unknown
NOT SUFFICIENT

IMO A

crimson_king

Joined: 21 Dec 2023

Last visit: 27 Apr 2026

Posts: 152

Own Kudos:

156

[1]

Given Kudos: 113

GRE 1: Q170 V170 Verified score

Posts: 152

Kudos: 156

[1]

30 Jun 2025, 08:28

Kudos

Bookmarks

Let the set of possible integers be S=x,x+1,...,y S = {x, x+1, ..., y} S=x,x+1,...,y.

The total number of possible choices for each person: n=y−x+1
Total possible pairs: n^2
Number of pairs where Ann's integer is greater than Bob's: For each possible value Ann can pick, count how many values Bob can pick that are less.

Let’s formalize:
For Ann to pick a number greater than Bob, Ann can pick any number from x+1 to y , and for each such number k, Bob can pick any number from x to k-1.

So the number of favorable pairs can be given as - number of favorable pairs/n^2 = (y-x)*(y-x+1)/2/(y-x+1)^2

Since we know the value of y-x=--9, we can formulate our answer for this question , hence 1 is sufficient.

For statement 2,
y=-20. We do not know x . The range could be any length, so the probability cannot be determined with this statement alone, hence we can rule out options (B) & (D).

Hence the answer is option (A)

A_Nishith

Joined: 29 Aug 2023

Last visit: 12 Nov 2025

Posts: 452

Own Kudos:

203

Given Kudos: 16

Posts: 452

Kudos: 203

30 Jun 2025, 08:31

Kudos

Bookmarks

Ann and Bob are selecting independently from the same set of integers: from x to y, inclusive.

The total number of integers =n=y−x+1

Let’s call the integers:x,x+1,x+2,...,y

Ann and Bob each pick one. We want to know the probability that Ann’s number is greater than Bob’s.

Note: If we know how many distinct integers are in the set, we can compute all possible outcomes and count the favorable ones (Ann > Bob).

🟩 Statement (1): y − x = 9
Then:

Number of integers = 9 + 1 = 10

So the set has 10 integers.

Since both are choosing uniformly from the same set of 10 integers, and we know the number of values, we can:

Calculate total outcomes: 10 × 10 = 100 pairs

Count favorable outcomes (Ann > Bob)

We don’t need to know x or y individually, only the number of values, which we have.

✅ Sufficient

🟩 Statement (2): y = -20
This tells us y, but nothing about x.

So we don’t know the size of the set of integers from x to y. Could be 1 number, 5 numbers, 100 numbers...

Without knowing x, we can’t compute how many integers are in the set → we cannot find the total number of possible outcomes.

🚫 Not sufficient

🟩 Combined:
(1) is already sufficient on its own, so we don’t need to combine.

✅ Final Answer: (A) — Statement (1) alone is sufficient, but statement (2) alone is not.

ManifestDreamMBA

Joined: 17 Sep 2024

Last visit: 21 Feb 2026

Posts: 1,387

Own Kudos:

898

[1]

Given Kudos: 243

Posts: 1,387

Kudos: 898

[1]

30 Jun 2025, 08:36

Kudos

Bookmarks

What is the probability that the integer Ann selects is greater than the one Bob selects?

S1
y - x = 9
This means there are a total of 10 integers to choose from
Now, total number of selections = 10*10 = 100
Out of these 100 scenarios, there will be 10 scenarios when both numbers are equal
Of the remaining 90 scenarios, owing to symmetry, there are exactly half of the scenarios when the values are greater for 90
So, P = 45/100 =.45
Sufficient

S2
y = -20
No info on x and hence, the range
Insufficient

Answer A

Bunuel

Ann and Bob each randomly select an integer from the integers x to y, inclusive. What is the probability that the integer Ann selects is greater than the one Bob selects?

(1) y - x = 9
(2) y = -20

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

chasing725

Joined: 22 Jun 2025

Last visit: 13 Jan 2026

Posts: 176

Own Kudos:

173

[1]

Given Kudos: 5

Location: United States (OR)

Schools: Stanford

Posts: 176

Kudos: 173

[1]

30 Jun 2025, 08:37

Kudos

Bookmarks

Bunuel

Ann and Bob each randomly select an integer from the integers x to y, inclusive. What is the probability that the integer Ann selects is greater than the one Bob selects?

(1) y - x = 9
(2) y = -20

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

(2) y = -20

Knowing one of the numbers is not sufficient. So, the easiest to eliminate is B and D.

(1) y - x = 9

The information tells us that there are 10 numbers in the series. Knowing this information is sufficient as we can find the probability.

Out of the number of subsets that can be created, half will have Ann > Bob

10C2/2*10 = 9/20

Sufficient

Option A

PGuha

Joined: 19 Aug 2024

Last visit: 25 Apr 2026

Posts: 14

Own Kudos:

Given Kudos: 13

Location: India

Schools: ISB INSEAD Aug '26 LBS '26 IESE '26 HEC Sept '26 Johnson '26 Kellogg '26

GMAT Focus 1: 555 Q81 V78 DI74 Verified score

GMAT Focus 2: 645 Q86 V82 DI79 Verified score

GPA: 8.56

Schools: ISB INSEAD Aug '26 LBS '26 IESE '26 HEC Sept '26 Johnson '26 Kellogg '26

GMAT Focus 2: 645 Q86 V82 DI79 Verified score

Posts: 14

Kudos: 1

30 Jun 2025, 08:37

Kudos

Bookmarks

I couldnt directly click on the correct option so my reply is E.

Bunuel

Ann and Bob each randomly select an integer from the integers x to y, inclusive. What is the probability that the integer Ann selects is greater than the one Bob selects?

(1) y - x = 9
(2) y = -20

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

Heix

Joined: 21 Feb 2024

Last visit: 24 Apr 2026

Posts: 465

Own Kudos:

167

[2]

Given Kudos: 63

Location: India

Concentration: Finance, Entrepreneurship

Schools: Ross MM "26 NUS Columbia '27

GMAT Focus 1: 485 Q76 V74 DI77 Verified score

GPA: 3.4

WE:Accounting (Finance)

Products:

Schools: Ross MM "26 NUS Columbia '27

GMAT Focus 1: 485 Q76 V74 DI77 Verified score

Posts: 465

Kudos: 167

[2]

30 Jun 2025, 08:38

Kudos

Bookmarks

First, let's understand what we're looking for. If Ann and Bob are each randomly selecting integers from the same range (x to y inclusive), we need to determine the probability that Ann's selection is greater than Bob's.
Statement 1: y - x= 9
This tells us the range has 10 integers (from x to y inclusive). However, we don't know the actual values of x and y. Let's see if we can determine the probability anyway.
For any two randomly selected integers from this range, there are a total of 10 × 10 = 100 possible outcomes (each person has 10 options). For Ann to select a greater number than Bob, we need to count the favorable outcomes.
If the range is [x, x+1, x+2, .., y), then for each value Bob selects, Ann needs to select a larger value. For example, if Bob selects x, Ann can select any of the 9 values greater than x. If Bob selects x+1, Ann can select any of the 8 values greater than x+1, and so on.
The number of favorable outcomes is: 9 + 8 + 7+6+5+4+3+2+1+0=45
So the probability is 45/100 = 9/20
Statement 1 alone is sufficient.
Statement 2: y = -20
This only tells us the upper bound of the range. Without knowing x, we can't determine how many integers are in the range, so we can't calculate the probability.
Statement 2 alone is not sufficient.
The answer is A) Statement 1 alone is sufficient, but statement 2 alone is not.

arbh77

Joined: 12 Apr 2025

Last visit: 15 Jul 2025

Posts: 12

Own Kudos:

[1]

Given Kudos: 9

Posts: 12

Kudos: 5

[1]

30 Jun 2025, 08:42

Kudos

Bookmarks

The answer is A.

The total number of integers they can choose from in this case would be y-x+1. (Eg: If I'm choosing numbers from 1 to 5 inclusive, I would do 5-1+1 which is 5. the numbers would be 1,2,3,4,5)

In this case because each of them randomly select an integer from x to y, the probability of them both choosing any integer would be the same. We also know that there would be some cases where they would choose the same number and it would be a tie. For eg: If they could choose any number from 1 to 3 - there would 3 cases where they could both choose the same number (1,1), (2,2),(3,3)

Since the probability of either of them getting an integer more than the other is the same, we can calculate the probability in which one would get more by

P = favourable outcomes / total outcomes

Favourable outcomes = n^2 - n where n^2 are the total number of possibilities and n are the number of ties as explained above.
Total outcomes = n^2 (for eg: in the example above, there would be 3 * 3 possibilities of choosing numbers)

So P = n^2-n/ n^2
Therefore, P = (y-x+1)^2 - (y-x+1)/ (y-x+1)^2.

Looking at options, in statement I: we see y-x is given to us so y-x+1 would be 10. We can therefore calculate the probability.
Statement II gives us the value of y but we know nothing about x so calculating probability is not possible.

Bunuel

Ann and Bob each randomly select an integer from the integers x to y, inclusive. What is the probability that the integer Ann selects is greater than the one Bob selects?

(1) y - x = 9
(2) y = -20

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

DataGuyX

Joined: 23 Apr 2023

Last visit: 02 Apr 2026

Posts: 111

Own Kudos:

[1]

Given Kudos: 161

Location: Brazil

Concentration: Entrepreneurship, Technology

Schools: Booth '26 (A$) Kellogg '26 (A) Sloan '26 (D) Stanford '26 (D) Haas '26 (D) HBS '26 (D)

GMAT Focus 1: 675 Q79 V85 DI86 Verified score

GPA: 7.3

Schools: Booth '26 (A$) Kellogg '26 (A) Sloan '26 (D) Stanford '26 (D) Haas '26 (D) HBS '26 (D)

GMAT Focus 1: 675 Q79 V85 DI86 Verified score

Posts: 111

Kudos: 77

[1]

30 Jun 2025, 08:43

Kudos

Bookmarks

Statement (1) With the range, given in the statement, we can calculate the probability for Ann for each possible choice of Bob. Example: if Bob pick the lowest number, Ann will have 8/9 chance. If Bob pick the second lowest, Ann will have 7/9 and so on. Since it's a DS question, I will stop here. Eliminate choices B, C, and E.

Statement (2) With the value of y we can not have any useful information to calculate the probabilities. Eliminate choice D.

Answer = A.

Prathu1221

Joined: 19 Jun 2025

Last visit: 20 Jul 2025

Posts: 62

Own Kudos:

Given Kudos: 1

Posts: 62

Kudos: 40

30 Jun 2025, 08:47

Kudos

Bookmarks

Now from 2nd statement substituting the values we will get x also so we get the range of integers which is x=-29 to y=-20. Now we can easily find the probablity of Ann selecting greater so answer would be Can be determined from both statements but not single statement alone.

Bunuel

Ann and Bob each randomly select an integer from the integers x to y, inclusive. What is the probability that the integer Ann selects is greater than the one Bob selects?

(1) y - x = 9
(2) y = -20

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

Dereno

Joined: 22 May 2020

Last visit: 27 Apr 2026

Posts: 1,398

Own Kudos:

1,374

[1]

Given Kudos: 425

Products:

Posts: 1,398

Kudos: 1,374

[1]

30 Jun 2025, 08:47

Kudos

Bookmarks

Bunuel

Ann and Bob each randomly select an integer from the integers x to y, inclusive. What is the probability that the integer Ann selects is greater than the one Bob selects?

(1) y - x = 9
(2) y = -20

This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

Let the number selected by Bob be n.

And n lies in the range x <= n <= y, where x,y are both integers.

We need to find : Probability that Integer selected by Ann is greater than the one Bob selects.

Statement 1:

(1) y - x = 9

y-x = 9, Hence, y = 9+x

x<= n <= 9+x

if x = 1, then y = 9+x = 9+1 =10

1 <= n <= 10.

if Bob selects, 1, Ann has 9 options 2,3,4,5,6,7,8,9,10.

if Bob selects 2, Ann has 8 options 3,4,5,6,7,8,9,10.

Probability of Ann selecting = 9(9+1)/2 = 45

Total probability of Ann = 45/100

Probability of Ann > Bob = Probabilty of Bob > Ann = 0.45

probability of both selecting same = 1-(0.45+0.45) = 0.10

Hence, Statement 1 is sufficient

Statement 2:

(2) y = -20

x can assume a wide array of values. Without any concrete value of x, we cannot find the probabilities.

Hence, insufficient

Option A

Tanish9102

Joined: 30 Jun 2025

Last visit: 20 Nov 2025

Posts: 59

Own Kudos:

Posts: 59

Kudos: 49

30 Jun 2025, 08:47

Kudos

Bookmarks

Answer: 9/10
Y= -20 and X= -29 (solving equation we get)
Now Anna and Bob can select from [-20,-29]
So Total we have 10 numbers and 9 cases can be made,
Answer is 9/10