A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car

Question

A collection of 36 cards consists of 4 sets of 9 cards each. The 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.
(2) The sum of the numbers on the remaining 35 cards is 176.

ID: 100993

romitsn · Accepted Answer

Total sum of numbers on 4 decks is  X4=180

1. only 180- 4 will be get you a units digit of 6. Hence 4 is the withdrawn card. --> Sufficient
2. 180 -4 =176 . Hence again 4 is the withdrawn card. --> Sufficient

Hence D

Bunuel · Answer

SOLUTION

A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9. If one cadrd has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6 --> we can get the sum of all 36 cards: sum=4(1+2+3+4+5+6+7+8+9) --> thus we can get which card should be removed so that the new sum to have the units digit of 6 (as cards are from 1 to 9). Sufficient.

(2) The sum of the numbers on the remaining 35 cards is 176 --> the same here. Sufficient.

Answer: D.

joe26219 · Answer

45 is the sum of each set (n(n+1)/2, n=9).Thus total sum would be 45*4 = 180.

Statement 1: subtracting x (x<=9) from 180 should give a units digit of 6, i.e. x=4 ---> Sufficient
Statement 2 : sum of remaining cards: 176, only 4 is left out. Sufficient

So D it is

kinjiGC · Answer

The value of the card can be 1 to 9. 
Statement 1) Sum of all the cards of one set = 1+2+..+9 = 9*10/2 = 45
So all the 4 sets = 4*45 = 180
last digit is 6 so card has to have a value of 4 because no other card number will satisfy the condition.

Statement 2) The sum is even more explicit. So definitely we can determine.

Hence option D)

EMPOWERgmatRichC · Answer

Hi All,

This question can actually be solved 'conceptually' - with very little math at all. However, the math involved is fairly low-level arithmetic, so here's how that math "works":

The sum of the integers from 1 to 9, inclusive = 45

Since we have 4 sets of those, the sum of ALL of the cards is 4(45) = 180

We're told that 1 card is removed and we're asked for the number on that card.

Fact 1: The units digit on the remaining cards is a 6.

With a total sum of 180, the ONLY card that we could remove and end up with a units digit of 6 is "a 4"

180 - 4 = 176.

Since the cards are numbered 1 through 9, there's no other card that can generate that same result.
Fact 1 is SUFFICIENT.

Fact 2: The sum on the remaining cards is 176.

Here, all of our prior work creates a 'shortcut' - we don't have to do any new work to deduce that the missing card was "a 4"
Fact 2 is SUFFICIENT.

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

BrentGMATPrepNow · Answer

Target question :    What is the number on the card?

Given : A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9.

Statement 1 : The units digit of the sum of the numbers on the remaining 35 cards is 6.  
1+2+3+4+5+6+7+8+9=45
Since there are 4 sets of cards numbered 1 to 9, the SUM of all 36 cards = 4(45) =  180

When we remove one card, the sum of the REMAINING 35 cards = --6 (units digit 6)
In other words,  180  - (value of chosen card) = --6
So,  the value of the chosen card must be 4 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : The sum of the numbers on the remaining 35 cards is 176.  
In other words,  180  - (value of chosen card) = 176
So,  the value of the chosen card must be 4 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

matteotchodi · Answer

I hope I can clarify for those that are having difficulty visualizing: Albert Einstein once said, “If I can't picture it, I can't understand it.”

A collection of 36 cards consists of 4 sets of 9 cards each. The 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.
(2) The sum of the numbers on the remaining 35 cards is 176.

solution:

recall: ONLY 10 digits exist.... the passage says there 4 sets of 9 cards... numbered 1 through 9....

so we have 
1 2 3 4 5 6 7 8 9 
1 2 3 4 5 6 7 8 9 
1 2 3 4 5 6 7 8 9 
1 2 3 4 5 6 7 8 9

notice each set is evenly spaced out... so we can apply the following rule S = A n... where the average = median... each set = 5 x 9 = 45

total sum 45 x 4 = 160 + 20 = 180

statement 1)

only 176 is possible this implies that we subtracted 4...… so we know a card with 4 was chosen (SUFFICIENT)

statement 2)

now this statement says we have 176 after subtracting the following means we chose 4 (SUFFICIENT)

NOTE: you do not need to know that the total sum of all the cards is 180..... I wrote that only for those that needed full comprehension of the problem

if you have a good understanding of number sense you can infer knowing the resulting units digit you have all the sufficient info to find what card was removed.... SINCE we have nine units digits all different from each other

for instance: say we have an integer that is 20

each of the following produces a result with a UNIQUE units digit.... test it

20 - 1
20 - 2
20 -3 
20 -4
20 -5 
20 - 6 
20 - 7 
20 - 8 
20 - 9

ScottTargetTestPrep · Answer

Solution:

Question Stem Analysis:

We need to determine the number on the card that is removed from the collection of 36 cards.

Statement One Alone:
 
Since the sum of all the numbers on the cards is (1 + 2 + 3 + … + 9) x 4 = 45 x 4 = 180, the units digit of this sum is 0. Therefore, if one card is removed and the units digit of the sum of the numbers on the remaining 35 cards is 6, the card that is removed must have the number 4. Statement one alone is sufficient.

Statement Two Alone:

From statement one, we see that the sum of the sum of all the numbers on the cards is 180. Therefore, if the sum of the numbers on the remaining 35 cards is 176, the card that is removed must have the number 4. Statement two alone is sufficient.

Answer: D

rushimehta · Answer

Of course, we can calculate and see that both statements are sufficient. But I wanted to highlight a logical approach that I observed post solving the question.

Statement (1): 
We know each card has a number from  1 to 9 , and there are 4 identical sets. So the total sum of all 36 cards is fixed (though we don't even need to calculate it).
When one card is removed, we’re told the  units digit of the remaining sum is 6 . Now, since all cards are numbered only from  1 to 9 , removing a single card means subtracting a number from 1 to 9 from the total. This subtraction will lead to a unique units digit in the remaining sum. For example:
 
 If total sum = 180 (for illustration), then (This works no matter what the total sum of all the cards is) :
 
 Remove 1 → 179 (units digit 9) 
 Remove 2 → 178 (units digit 8) 
 ... 
 Remove 4 → 176 (units digit 6) 
 ...  
  
So if the resulting units digit is 6, we can  uniquely identify  that the removed number was  4 .

In this case, if we had a card numbered 10 in the set... then also we would have been able to uniquely identify the removed number based on the units digit (this is possible because we don't have a card numbered as 0 --> if we had, removing a card numbered 0 or 10, both would provide us with the same units digit, and thus the number on card removed would be indistinguishable by units digit alone)

Had the cards included higher numbers, greater than 10, like 11, 12, etc., the  units digit would not uniquely identify  the removed card. 
For instance, 180 – 1 = 179 and 180 – 11 = 169 → both end in 9. So 1 and 11 would be indistinguishable by units digit alone.

But in this case, because the numbers are  strictly 1 through 9 , knowing the units digit of the remaining sum is enough to uniquely identify the removed card.

Statement (2): 
Same logic applies. If the total sum is 180 (which it is: 4 × (1+2+...+9) = 4 × 45 = 180), and the sum of remaining 35 cards is  176 , then the removed card is clearly  4 .

So... Even without calculating the total, the constraint that card numbers range from 1 to 9 ensures that  each possible removal leaves a distinct final units digit . That’s what makes both statements  individually sufficient .

A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

A collection of 36 cards consists of 4 sets of 9 cards each. The 9 car

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards