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555-605 (Medium)|   Math Related|         
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geocircle
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12 Days of Christmas GMAT Competition 2025 - Day 9: A museum issued a 26 Dec 2025, 07:26
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Let's do total = 100

Never activated = 15
Activated = 85

Family pases = 40% of 85 = 34
Individual passes = 60% of 85 = 51

A = 21/34 * 34 = 21
B = 1/3 * 51 = 17

A=21 and B=17
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12 Days of Christmas GMAT Competition 2025 - Day 9: A museum issued a 26 Dec 2025, 07:29
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Bunuel
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A museum issued a certain number of annual passes. 15% of the passes were never activated. Of the activated passes, 40% were Family passes and 60% were Individual passes. Among the activated passes, 21/34 of the Family passes and 1/3 of the Individual passes were used fewer than 6 times during the month.

Of all passes issued, A percent are Family passes that were used fewer than 6 times during the month, and B percent are Individual passes that were used fewer than 6 times during the month.

Select for A and for B the options that complete the statement so that it is most accurate based on the information provided. Make only two selections, one in each column.
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Let total no of passes=100
12% never activated=15
85% activated= 85
40% of activated pass is family pass- 0.4x85=34
60% of activated pass individual pass-0.6x85=51
family passes used fewer than 6 times= 21/34 x34=21%
individual passes used fewer than 5 times = 1/3 x51=17 %
Ans. A=21 B= 17
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12 Days of Christmas GMAT Competition 2025 - Day 9: A museum issued a 26 Dec 2025, 07:30
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A museum issued a certain number of annual passes. 15% of the passes were never activated. Of the activated passes, 40% were Family passes and 60% were Individual passes. Among the activated passes, 21/34 of the Family passes and 1/3 of the Individual passes were used fewer than 6 times during the month.

Of all passes issued, A percent are Family passes that were used fewer than 6 times during the month, and B percent are Individual passes that were used fewer than 6 times during the month.

Select for A and for B the options that complete the statement so that it is most accurate based on the information provided. Make only two selections, one in each column.
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consider Family passes as 34, proportionately (34*6)/4 = total individual passes = 51
Family passes
<6 = 21
>=6 13

Individual passes
<6 = 17
>=6 34

Activated = 85, total = 100

Correct Answer
A = 21
B = 17
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12 Days of Christmas GMAT Competition 2025 - Day 9: A museum issued a 26 Dec 2025, 07:35
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Let P= 100 be the total number of passes issued by the museum.

Then A = 4/10 *P*85/100*rate_fewer and B = 6/10*P*85/100*rate_fewer

we know that the number of P passes used less than 6 times during the month are 21/34 for A while for B 1/3

plugging P = 100 we get A = 21 and B = 17
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12 Days of Christmas GMAT Competition 2025 - Day 9: A museum issued a 26 Dec 2025, 07:35
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Let annual passes be 'x'
Never activated = 0.15x
Activated = 0.85x

Family Passes = 40% of activated passes = 0.4 * 0.85x = 0.34x
Individual passes = 0.6 * 0.85x = 0.51x

Now it is given that used fewer than 6 times during the month is
Family passes = 21/34 * 0.34x = 0.21x
Hence A = 100*0.21x/x = 21%

Individual passes = 1/3*0.51x = 0.17x
And B = 100*0.17x/x = 17%


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A museum issued a certain number of annual passes. 15% of the passes were never activated. Of the activated passes, 40% were Family passes and 60% were Individual passes. Among the activated passes, 21/34 of the Family passes and 1/3 of the Individual passes were used fewer than 6 times during the month.

Of all passes issued, A percent are Family passes that were used fewer than 6 times during the month, and B percent are Individual passes that were used fewer than 6 times during the month.

Select for A and for B the options that complete the statement so that it is most accurate based on the information provided. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition 2025 - Day 9: A museum issued a 26 Dec 2025, 07:41
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assuming p as pass and following through the question:
not activated = 0.15p, activated = 0.85p
of 0.85p -> family plan: 0.4*0.85p | individual plan: 0.6*0.85p
21/34 of family plan (A) | 1/3 of individual plan (B) used less than 6 times during the month
on calculating -> A = 21p/100 and B = 17p/100.
A = 21 and B = 17 if p = 100.
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12 Days of Christmas GMAT Competition 2025 - Day 9: A museum issued a 26 Dec 2025, 07:46
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Number of annual passes = 100
No activated = 15 -> activated = 100-15 = 85

Family = 0.4*85 = 34
Individual = 0.6*85 = 51

Family<6 = 34 * 21/34 = 21
Individual<6 = 51/3 = 17

A=21
B=17
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12 Days of Christmas GMAT Competition 2025 - Day 9: A museum issued a 26 Dec 2025, 08:03
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This one felt relatively simple. Present from Santa Bunuel :P?

A museum issues a certain number of annual passes.

Let's take x as the number of passes.

15% were never activated - 85% were. (0.15x passes were never activated, 0.85x were)

Of the activated passes (0.85x), 40% (0.34x) were family passes and the remaining 60% (0.51x) were individual passes.

Among the activated passes - 21/34 of the family passes and 1/3 of the Individual passes were used fewer than 6 times a month.

Now, 21/34 isn't 21 out of the 34 passes, but still, a ratio.

So, hence, we multiply the ratio: to the variable:

21/34 (0.34x) = 21 (0.01)x = 0.21x.

So, 21% of the total number of passes were used less than 6 times a month. (A)

Similarly, 1/3*(0.51) = 17% of the total passes were used less than 6 times a month. (B)



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A museum issued a certain number of annual passes. 15% of the passes were never activated. Of the activated passes, 40% were Family passes and 60% were Individual passes. Among the activated passes, 21/34 of the Family passes and 1/3 of the Individual passes were used fewer than 6 times during the month.

Of all passes issued, A percent are Family passes that were used fewer than 6 times during the month, and B percent are Individual passes that were used fewer than 6 times during the month.

Select for A and for B the options that complete the statement so that it is most accurate based on the information provided. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition 2025 - Day 9: A museum issued a 26 Dec 2025, 08:07
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Let total passes issued = 100.
Activated vs not activated: 15% never activated and 85% activated
Of activated passes Of the activated passes (85):
Family = 40% of 85 = 34
Individual = 60% of 85 = 51

Used fewer than 6 times:
Family passes:
21/34 of 34
A = (21/34) × 34 = 21
So, A = 21%

Individual passes: 1/3 of 51
B = (1/3) × 51 = 17
So, B = 17%
Final Answer should be A = 21 B = 17.
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A museum issued a certain number of annual passes. 15% of the passes were never activated. Of the activated passes, 40% were Family passes and 60% were Individual passes. Among the activated passes, 21/34 of the Family passes and 1/3 of the Individual passes were used fewer than 6 times during the month.

Of all passes issued, A percent are Family passes that were used fewer than 6 times during the month, and B percent are Individual passes that were used fewer than 6 times during the month.

Select for A and for B the options that complete the statement so that it is most accurate based on the information provided. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition 2025 - Day 9: A museum issued a 26 Dec 2025, 08:07
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It's easier to use numbers than percentages.

Annual pases = 100, 15 never activated and 85 activated.

85 activated: 40% are Family passes (34) and 60% are Individual passes (51).

34 Family passes: 21/34 * 34 = 21 were used fewer than 6 times during the month.

51 Individual passes: 51/3 = 17 were used fewer than 6 times during the month.

A=21 and B=17
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12 Days of Christmas GMAT Competition 2025 - Day 9: A museum issued a 26 Dec 2025, 08:11
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Activated passes

40% of 85% = 34% family passes
60% of 85% = 51% individual passes

A% = 21/34*34% = 21% family passes used fewer than 6 times a month
B% = 1/3*51% = 17% individual passes used fewer than 6 times a month

So A=21 B=17

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A museum issued a certain number of annual passes. 15% of the passes were never activated. Of the activated passes, 40% were Family passes and 60% were Individual passes. Among the activated passes, 21/34 of the Family passes and 1/3 of the Individual passes were used fewer than 6 times during the month.

Of all passes issued, A percent are Family passes that were used fewer than 6 times during the month, and B percent are Individual passes that were used fewer than 6 times during the month.

Select for A and for B the options that complete the statement so that it is most accurate based on the information provided. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition 2025 - Day 9: A museum issued a 26 Dec 2025, 08:50
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Let total passes issued = 100

Never Activated = 15% = 15
Activated = 85

Of these 85 activated passes,
40% were family = 0.4*85 = 34
60% were individual = 0.6*85 = 51

Family passes: fractions used fewer than 6 times = 21/34
Total = 21/34 * 34 = 21

Number of individuals used who used fewer than 6 times = 1/3*51 = 17

A = 21
B= 17
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A museum issued a certain number of annual passes. 15% of the passes were never activated. Of the activated passes, 40% were Family passes and 60% were Individual passes. Among the activated passes, 21/34 of the Family passes and 1/3 of the Individual passes were used fewer than 6 times during the month.

Of all passes issued, A percent are Family passes that were used fewer than 6 times during the month, and B percent are Individual passes that were used fewer than 6 times during the month.

Select for A and for B the options that complete the statement so that it is most accurate based on the information provided. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition 2025 - Day 9: A museum issued a 26 Dec 2025, 08:53
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Let total passes be x

A% of x = (21/34) of 40% of 85% of x
= 21% of x

B% of x = (1/3) of 60% of 85% of x
= 17% of x

Hence (A) is 21 and (B) is 17
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