Problem solving question with answer
What is the 173rd digit to the right of the decimal point in the standard decimal expansion of 234567/7 ?
a) 1
b) 2
c) 5
d) 8
e) 9
First, do the division (you need to get fast at doing calculations on paper!) to obtain the repeating sequence of digits after the decimal: 571428. That is 234567/7 = 33509.5714857148
Then, divide the total number of digits the question asks for by the length of the sequence 571428 (the number of terms in this sequence is 6) : 173/6
The remainder when 173 is divided by 6 is 5.
Thus, the answer is the 5th digit in the sequence: 2. ANSWER B
Keep in mind that finding patterns is an important part of the GMAT. During our classes we go into more detail about finding patterns, and how do deal with remainders which would make this question easier.
Data Sufficiency question with asnwer
Example:
If x, y, and z are positive integers, is the sum of x and y divisible by 3?
1) The sum of x and z is divisible by 3
2) The sum of y and z is divisible by 3
(ANSWER E)
For the sum of x and y to be divisible by 3, the sum of the remainders of x and y (when
they’re divided by 3) must be equivalent to 0 upon division by 3.
Statement 1: gives no information about y, and so is clearly Not Sufficient
but the remainder of x could be 0, and the remainder of z could be 0
or the remainder of x could be 1, and the remainder of z could be 2
or the remainder of x could be 2, and the remainder of z could be 1
Statement 2: gives no information about x, and so is clearly Not Sufficient
but the remainder of y could be 0, and the remainder of z could be 0
or the remainder of y could be 1, and the remainder of z could be 2
or the remainder of y could be 2, and the remainder of z could be 1
Statements 1&2: if both statements are true, this means that x and y have the remainder
under division by 3.
If that remainder = 0, the answer is yes
If that remainder = 1, the answer to the question is no
Not Sufficient
Reading Comprehension questions with answers
- The primary purpose of the passage is to
- dissect a confusing matter of foreign policy
- draw attention to an abnormality
- clarify an ambiguity
- rank economic influences
- provide an example of colonial hypocrisy
Answer B is correct. The focus of the first paragraph is to show why Europeans acquired colonies and what these colonies usually did. Then the author goes on to show why the colonies in the Philippines where an anomaly or an abnormality. Therefore, B is not wrong but it’s a good idea to check that the other answers are not right.
Answer A is incorrect. While the passage may seem confusing upon first glance, the policy that Spain followed is clear, they focused on commerce in the colony and they wanted to hold on to the area. What is not clear is why they wanted to hold on to the colony because at the time it was unusual or abnormal for a colony to be used for reasons other than agriculture and mining.
Answer C is incorrect. Here the author doesn’t really clarify why the Spanish did what they did. He said that “perhaps” the Spanish held the Philippines for religious or strategic reasons but we aren’t told for sure.
Answer D is incorrect. The passage does talk about the priorities economically speaking for most colonies, but this information is used primarily to show how odd the Spanish colonies in the Philippines were compared to most colonies.
Answer E is incorrect. The example that is shown is not hypocritical, but rather just different from what is expected.
- The passage suggests that if non-mercantilist reasons were behind the decision to continue to hold the Philippines, then one would expect which of the following to be true?
- Spanish religious beliefs were incompatible with colonial objectives.
- Spain received a significant amount of gold and silver from the Philippines.
- The Philippines were located in a place of unique military interest.
- Spain had sufficient domestic natural resources so as to be indifferent to what the Philippines might otherwise have contributed.
- Spain had plans to move away from an agriculture-based economy.
Answer C is correct. At the end of the passage we are told that the non-mercantilist reasons of religion or strategy were perhaps why Spain held the Philippines. The Philippines having a unique military interest is therefore one possible strategic reason to keep the islands.
Answer A is incorrect. This answer is simply stating a fact: religious beliefs were usually incompatible with colonial objectives. This answer does not show us what we would expect to be true based on the decision to hold the Philippines. For example, we would possibly expect that the Spanish wanted to convert the native people for religious reasons.
Answer B is incorrect. Gold and silver are mercantilist reasons for holding a colony and we are trying to figure out what we could expect to be true given non-mercantilist reasons for keeping the Philippines.
Answer D is incorrect. If non-mercantilist reasons are behind holding the Philippines then we would probably expect a strategic or religious reason for keeping the islands. Being indifferent is a non-mercantilist reason for holding an island, but not one that we would expect.
Answer E is incorrect. Planning on moving away from an agriculture-based economy could be one reason for holding the Philippines, but there is nothing in the passage to suggest that we could expect that the Spanish where planning on doing this.
- According to the passage, which of the following would provide the best evidence of successful mercantilist colonization?
- A colony rich in iron ore deposits
- A colony that gradually develops into a significant port of trade
- A colony that innovates a revolutionary agricultural process
- A colony with a vibrant religious history
- A colony with significant military capability
Answer A is correct. In the passage we are told that mercantilist colonization revolved around the accumulation of precious metals such as, but not limited to, gold and silver. Iron could also be considered a precious metal and therefore A is not wrong. Here again though, it would be good to eliminate the other answer choices to make sure it’s the right answer.
Answer B is incorrect. Mercantilist colonization revolves around either acquiring precious metals, land, and/or natural resources. Becoming a port of trade therefore, would not be considered successful mercantilist colonization. (The passage states that the Philippines became a port of trade, but that this was unusual since it didn’t fit the normal mercantilist goals.)
Answer C is incorrect. The passage does say that agricultural and/or natural resource acquisition would be evidence of a successful mercantilist colony. However, this answer talks about innovating a revolutionary agricultural process, no acquiring new land. Therefore, it is incorrect.
Answer D is incorrect. While Spain may have kept the Philippines for religious reasons, the passage does not say that this would be the best evidence of a successful mercantilist colonization. In fact, many mercantilists wouldn’t consider this successful at all.
Answer E is incorrect. Spain may have kept the Philippines for military reasons, but the passage does not say that this would be the best evidence of a successful mercantilist colonization. Instead, mecantilist generally focused on mercantilist the accumulation of precious metals and of natural resources.
Critical Reasoning question with answer
Example: It is commonly accepted that socioeconomic status (SES) plays a role in language development. As a general rule, children of lower-SES families have less-developed vocabularies and lower language proficiency scores than do children who are raised in more advantageous situations. Yet new research suggests that SES is not the most important factor in a child’s language development—rather, it is whether parents actively talk to their toddler or not. Raising children with better language processing efficiency and stronger vocabularies has almost nothing to do with SES, then; parents simply need to talk directly to their toddlers.
Which of the following, if true, casts the most doubt on the effectiveness of the conclusion drawn above?
- Toddlers who watched more dialogue-heavy television did not demonstrate any gains in language development.
- Toddlers from lower-SES families often spend up to 500% more time in daycare centers than with their parents.
- Toddlers with bilingual parents tend to speak much later than their monolingual peers.
- Parents from higher-SES backgrounds tend to have fewer children.
- Toddlers from lower-SES families tend to own fewer books than do their higher-SES peers.
Answer : B
This question asks us to weaken the argument: “Raising children with better language processing efficiency and stronger vocabularies has almost nothing to do with SES, then; parents simply need to talk directly to their toddlers.” This argument is drawn from research stating that parents actively talking to their children is a more important factor in language development than SES is. However, we don’t know if these two factors are in any way related. Answer A addresses an issue that might arise in our heads while reading the question, of whether TV might be a substitute for talking directly with children. This issue is not raised in the passage, though. Answer C might confuse us into thinking that bilingual parents would speak to their children more than monolingual parents, in which case it would cast doubt on the statement; but we know of no difference between the amount bilingual parents speak to their children. Answer D provides a weakening argument, but only if we assume that having fewer children means that their parents have more time to devote to speaking to each one. Because this isn’t given, we must reject D. And Answer E increases the scope and introduces a line of argument related to reading, which is tangential to the statement. We choose Answer B because it shows that SES is strongly correlated with the amount of time parents spend with their children, during which they would have the opportunity to speak to their children, and thus weakening the argument that SES has almost nothing to do with language development.
Sentence Correction question with answer
Example: Nazi occupying powers in Eastern Europe practiced a policy of collective punishment, destroying entire villages for acts of sabotage even though all their inhabitants did not participate in them.
A. all their inhabitants did not participate in them
B. not all their inhabitants participated in them
C. all their inhabitants may not have participated in them
D. not all their inhabitants would have participated in them
E. all their inhabitants were not participating in them
Negation; verbs—tense.
To structure a sentence like this, ask yourself which thing should take the negation. It’s rather awkward and confusing to introduce a group of “all” people and then try to explain that some people do something and some do not by negating the verb (“did not participate”). In this case, it’s better to negate the subject of the phrase “not all their inhabitants” and leave the verb alone.
A. This is confusing. Did none of the inhabitants participate or some of them?
B. Correct.
C. This repeats the same mistake as the original, but use of the present perfect tense is incorrect.
D. This puts the negation in the correct place, but use of the conditional is incorrect.
E. This repeats the mistake of the original and there is no need to use the past continuous tense.
