Every year, during Tom's birthday, his grandmother kisses him as many kisses she kissed him during his previous birthday, less his age (a kiss for each year.) How many kisses did Tom receive from his grandmother on his 15th birthday?
(1) Tom received 144 kisses from his grandmother during his first (age 1 year) birthday.
(2) On his 11th birthday, Tom received 10% less kisses from his grandmother than he did on his 10th birthday.
OA is D
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Every year, during Tom's birthday, his grandmother kisses hi
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sachin_yadav
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Hi sachin_yadav,
This question is a non-typical Sequence question. The 'rules' are clearly defined, but we need some type of numeric data to answer the given question. Knowing the number of kisses he received on any given birthday would obviously be enough information to answer this question, but 'ratio data' would also provide the necessary information.
We're asked for the number of kisses that Tom received on his 15th birthday. Based on the information in the prompt, we know that THIS number will be 15 less than the number on his 14th birthday (and the number he received on his 14th birthday will be 14 less than the number he received on his 13th birthday, etc.).
1) Tom received 144 kisses from his grandmother during his first (age 1 year) birthday.
With this Fact, we can 'subtract down' each year until we hit the 15th year....
Yr. 1 = 144 kisses received
Yr. 2 = 144-2 = 142 kisses
Yr. 3 = 142-3 = 139 kisses
Yr. 4 = 139-4 = 135 kisses
Etc.
We will eventually get to the exact number he received on his 15th birthday.
Fact 1 is SUFFICIENT
2) On his 11th birthday, Tom received 10% less kisses from his grandmother than he did on his 10th birthday.
This Fact might appear insufficient at first, but you have to really think about what it's telling you. Since we know how many FEWER kisses he receives each year, you have to consider what "EXACTLY 10% less kisses" translates into...
On his 11th birthday, he receives 11 less kisses than he did on his 10th birthday. THAT number is equal to 10% less kisses:
X = number of kisses received on 10th birthday
(X-11) = number of kiss on his 11th birthday
(X - 11) = X - (.1)(X)
X - 11 = .9X
.1X = 11
X = 110
Now we know how many kisses he received on his 10th birthday, so we can 'subtract down' to his 15th birthday.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This question is a non-typical Sequence question. The 'rules' are clearly defined, but we need some type of numeric data to answer the given question. Knowing the number of kisses he received on any given birthday would obviously be enough information to answer this question, but 'ratio data' would also provide the necessary information.
We're asked for the number of kisses that Tom received on his 15th birthday. Based on the information in the prompt, we know that THIS number will be 15 less than the number on his 14th birthday (and the number he received on his 14th birthday will be 14 less than the number he received on his 13th birthday, etc.).
1) Tom received 144 kisses from his grandmother during his first (age 1 year) birthday.
With this Fact, we can 'subtract down' each year until we hit the 15th year....
Yr. 1 = 144 kisses received
Yr. 2 = 144-2 = 142 kisses
Yr. 3 = 142-3 = 139 kisses
Yr. 4 = 139-4 = 135 kisses
Etc.
We will eventually get to the exact number he received on his 15th birthday.
Fact 1 is SUFFICIENT
2) On his 11th birthday, Tom received 10% less kisses from his grandmother than he did on his 10th birthday.
This Fact might appear insufficient at first, but you have to really think about what it's telling you. Since we know how many FEWER kisses he receives each year, you have to consider what "EXACTLY 10% less kisses" translates into...
On his 11th birthday, he receives 11 less kisses than he did on his 10th birthday. THAT number is equal to 10% less kisses:
X = number of kisses received on 10th birthday
(X-11) = number of kiss on his 11th birthday
(X - 11) = X - (.1)(X)
X - 11 = .9X
.1X = 11
X = 110
Now we know how many kisses he received on his 10th birthday, so we can 'subtract down' to his 15th birthday.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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Matt@VeritasPrep
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This is basically a sequence problem. Let's say that k0 (the number of kisses when Tom was born, i.e. his 0th birthday) = x. From there, we have
k0 = x
k1 = x - 1
k2 = (x - 1) - 2
k3 = (x - 1 - 2) - 3,
etc.
So the number of kisses Tom gets each birthday = x - (the sum of the ages ≤ his new age on this birthday).
S1::
x = 144
Sufficient, as we only needed to know x: everything else in our sequence is an integer.
S2::
k11 = .9 * k10
Since k11 = (x - 1 - 2 - 3 - ... 11) and k10 = (x - 1 - 2 - 3 - ... - 10), this is an equation in a single variable (x), so we can solve again! Sufficient, and we're done.
k0 = x
k1 = x - 1
k2 = (x - 1) - 2
k3 = (x - 1 - 2) - 3,
etc.
So the number of kisses Tom gets each birthday = x - (the sum of the ages ≤ his new age on this birthday).
S1::
x = 144
Sufficient, as we only needed to know x: everything else in our sequence is an integer.
S2::
k11 = .9 * k10
Since k11 = (x - 1 - 2 - 3 - ... 11) and k10 = (x - 1 - 2 - 3 - ... - 10), this is an equation in a single variable (x), so we can solve again! Sufficient, and we're done.
